Resources

Resources

Euler's method

m \angle 3=111

m \angle 14

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69

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111

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180

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90

y=5 ext{cos}(2x+10)

Find rac{d^2y}{dx^2}

g(x)=x^{3}+12x^{2}+36x

c

be the number that satisfies the Mean Value Theorem for

g

on the interval

-8 \leq x \leq -2

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c

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1

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-7

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-6

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-3

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-1

y=f(x)

be the solution to the differential equation

\frac{dy}{dx}=1+2y

with the initial condition

f(0)=1

. What is the approximation for

f(1)

if Euler's method is used, starting at

x=0

with a step size of

0.5

x=\frac{5\pi}{6}+k\pi

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Solve the equation in the interval

0 \leq x < 2\pi

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3\tan x-\sqrt{3}=0

The particular solution of the differential equation

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\frac{dy}{dx}=\frac{y+1}{x^{2}-x}

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x=2

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y=1

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xy=4x-6

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xy=2x-2

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xy=x-2

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xy=-x+4

\lim _{h \rightarrow 0} \frac{2 \sqrt[3]{8+h}-2 \sqrt[3]{8}}{h}

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1

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\frac{1}{12}

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\frac{1}{6}

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4

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(D) The limit doesn't exist

4 x-x^{2} y+y^{3}=10

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Find the value of

\frac{d y}{d x}

(1,2)

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1

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-4

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\frac{2}{3}

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-1

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0

\frac{d y}{d t}=y+1 \text { and } y(0)=3 \text {. }

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t

y=1

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1

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t=1

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t=-\ln 2

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t=\ln 2

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t=\ln 4

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t=0

\frac{d y}{d t}=y+1 \text { and } y(0)=3 \text {. }

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t

y=1

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1

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t=0

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t=\ln 2

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t=-\ln 2

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t=1

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t=\ln 4

\frac{1}{2}c^{2}+3c=1

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c=f

c=g

be the solutions to the given equation. If

f > g

, which of the following is the value of

f

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1

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-3+\sqrt{2}

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-3+\sqrt{11}

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3+\sqrt{2}

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3+\sqrt{11}

\sum_{k=0}^{19} 6(1.5)^{k} \approx

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1

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7983

02

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13,301.03

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26,590.05

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39,891.08

\frac{d y}{d t}=2 t+3 \text { and } y(1)=6 .

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t

y=0

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Choose all answers that apply:

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t=-3

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t=-1

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t=1

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t=0

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t=-2

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t=-4

Express the following rational numbers in the form

\frac{p}{q}

p

q

q\neq 0

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6.\overline{46}

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0.1\overline{36}

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3.\overline{146}

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-5.\overline{12}

Express the following rational numbers in the form

\frac{p}{q}, p, q

q \neq 0

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6 . \overline{46}

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0 . \overline{136}

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3 . \overline{146}

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-5 . \overline{12}

Re-arrange the following equation to make

C

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e=i r+\frac{Q}{C}

P = \{-10, -9, -8\}

Q = \{-9, -8, -7, -6, -5\}

P \cap Q

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\{-10, -9, -8, -5\}

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\{-8\}

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\{-9, -8\}

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\{-10, -9, -8, -7, -6, -5\}

Q = \{3, 6, 9, 12\}

R = \{15\}

Q \cup R

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\{3, 6, 9, 12, 15\}

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\emptyset

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\{3, 6, 9\}

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\{12, 15\}

E = \{2, 6\}

F = \{1, 3, 4, 5, 7\}

E \cap F

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\emptyset

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\{1, 2, 3, 4, 5, 6, 7\}

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\{1, 2, 5, 6\}

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\{1, 2, 5, 6, 7\}

D = \{5\}

E = \{5, 15, 25, 35\}

D \cup E

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\{5, 15, 25, 35\}

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\{15, 25, 35\}

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\{25\}

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\emptyset

P = \{-10, -9, -8\}

Q = \{-9, -8, -7, -6, -5\}

P \cap Q

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\{-10, -9, -8, -5\}

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\{-9, -8\}

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\{-8\}

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\{-10, -9, -8, -7, -6, -5\}

D = \{8, 14\}

E = \{0, 4, 18\}

D \cap E

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\{0\}

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\{0, 4, 8, 14, 18\}

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\{0, 4, 8, 18\}

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\emptyset

J = \{-7, -6, -2, 0, 1, 5\}

K = \{-4, -1, 2\}

J \cap K

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\{-7, -6, -4, -2, -1, 0, 1, 2, 5\}

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\{-4, -2, -1, 0, 1, 2, 5\}

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\{-7, -6, -1, 0, 1, 5\}

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\emptyset

G = \{-9, 9\}

H = \{-10, -9\}

G \cap H

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\{-10\}

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\{-9\}

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\{-10, -9, 9\}

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\{-10, 9\}

R = \{4, 8, 12, 16\}

S = \{2, 6, 10, 14, 20\}

R \cap S

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\{2, 4, 6, 8, 10, 12, 14, 16, 20\}

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\emptyset

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\{2, 4, 6, 8, 10, 12\}

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\{4, 20\}

D = \{1, 4\}

E = \{0, 1, 2, 3, 4\}

D \cap E

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\{4\}

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\{0, 1, 2, 3, 4\}

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\{1, 4\}

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\{1, 2, 3, 4\}

J = \{1, 3, 5, 7, 9\}

K = \{2\}

J \cup K

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\{1, 2, 3, 5, 7, 9\}

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\emptyset

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\{2, 9\}

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\{1, 5, 7\}

\frac{1}{6} \sqrt{k}-3=1-\sqrt{k}

, approximately what is the value of

k

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1

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1

9

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2

9

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3

4

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11

8

Which of the following are rational numbers?

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Multi-select Choices:

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\frac{5}{7}

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\frac{2}{7}

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\sqrt{8}

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0

-(a-1)(b-1)(c-1)

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Which of the following is equivalent to the given expression?

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1

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(1-a)(b-1)(1-c)

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(1-a)(1-b)(1-c)

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(a-1)(1-b)(1-c)

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(1-a)(1-b)(c-1)

2

y(x-1)=z

x=

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1

y-z

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2

z / y+1

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3

y(z-1)

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4

z(y-1)

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5

1

zy

\begin{aligned} 44(j+2 k) & =12 \\ 22 k & =-11 j+16 \end{aligned}

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Consider the system of equations. How many solutions

(j, k)

does this system have?

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1

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0

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1

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2

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(D) Infinitely many

Let y be defined implicitly by the equation.

-10 x^{3}-8 y^{3}-x-10 y=-91 \text {. }

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Use implicit differentiation to find

\frac{d y}{d x}

Which of the following is the derivative

\frac{d y}{d x}

for the plane curve defined by the equations

x(t)=\frac{1}{2} \sin 2 t

y(t)=2 \cos 2 t

0 \leq t \leq 2 \pi

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Select the correct answer below:

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4 \cot 2 t

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\tan 4 t

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-\tan 4 t

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-4 \tan 2 t

\frac{1}{3}x+3y=4

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2x-4=2y

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Consider the given system of equations. If

(x,y)

is the solution to the system, then what is the value of

x-y

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\square

Dante commutes to work

4

mornings a week. For his commute each morning, he walks for

10

minutes, waits and rides the bus for

x

minutes, and waits and rides the train for

y

minutes. If Dante spends at least

3.5

hours on his morning commute each week, which of the following inequalities best describes Dante's weekly morning commute?

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1

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x+y+10 \geq 3.5(60)

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x+y+10 \geq 3.5(60)(4)

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4(x+y)+10 \geq 3.5(60)

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4(x+y+10) \geq 3.5(60)

1,000=20z^{2}

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How many distinct real solutions does the given equation have?

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1

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0

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1

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2

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4

y^{\prime}=0.5(100-y)

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y=5 e^{-0.5 x}+100

a solution to the above equation?

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1

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What is the area of the region between the graphs of

f(x)=\sqrt{x+10}

g(x)=x-2

x=-10

x=6

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1

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\frac{320}{3}

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128

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\mathbf{1 6 0}

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\frac{64}{3}

What is the area of the region between the graphs of

f(x)=x^{2}-4 x+1

g(x)=3 x-5

x=1

x=4

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1

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\frac{125}{6}

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4

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\frac{27}{2}

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\frac{81}{2}

f(x)=-4 x^{3}+6 x^{2}+1

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What is the absolute minimum value of

f

over the closed interval

-4 \leq x \leq 3

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1

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3

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-78

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-353

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-53

f(x)=2 x^{3}+21 x^{2}+36 x

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What is the absolute maximum value of

f

over the closed interval

[-8,0]

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1

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0

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108

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180

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32

h(x)=2 x^{3}+3 x^{2}-12 x

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What is the absolute minimum value of

h

over the closed interval

-3 \leq x \leq 3

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1

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-32

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-45

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-7

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20

h(x)=-2 x^{3}-7

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The absolute maximum value of

h

over the closed interval

[-3,2]

x

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1

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1

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-2

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2

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-3

h(x)=-2 x^{3}-7

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The absolute maximum value of

h

over the closed interval

[-3,2]

x

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1

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-3

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2

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1

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-2

h(x)=x^{3}+6 x^{2}+2

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What is the absolute minimum value of

h

over the closed interval

-6 \leq x \leq 2

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1

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34

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2

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-34

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-2

g(x)=-2 x^{3}+3 x^{2}+36 x

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The absolute maximum value of

g

over the closed interval

[-3,5]

x

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1

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5

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2

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3

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-3

g(x)=2 x^{3}-21 x^{2}+60 x

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What is the absolute maximum value of

g

over the closed interval

[0,6]

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1

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25

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42

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36

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52

h(x)=x^{3}-6 x^{2}+8

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The absolute minimum value of

h

over the closed interval

-1 \leq x \leq 6

x

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1

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-1

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6

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4

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0

g(x)=x^{3}-12 x+7

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The absolute maximum value of

g

over the closed interval

[-4,5]

x

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1

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5

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-2

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2

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-4