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Resources

Find derivatives of sine and cosine functions

Solve for the exact value of

x

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3 \ln (2 x-2)+14=5

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The focal length,

F

, of a camera's lens is related to the distance of the object from the lens.

I

and the distance to the image area in the camera,

W

, by the formula below.

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\frac{1}{J}+\frac{1}{W}=\frac{1}{F}

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When this equation is solved for

J

F

W

J

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(1)

(F-W)

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(2)

\frac{FW}{F+W}

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(3)

\frac{FW}{F-W}

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(4)

\frac{1}{F}

\frac{1}{W}

Find the derivative of

f(x)

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\begin{array}{l} f(x)=x \sin (x) \\ f^{\prime}(x)= \end{array}

Approximate the definite integral by right Riemann sum with the indicated partitions.

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y=\cos x

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[0,\frac{\pi}{6},\frac{\pi}{4},\frac{\pi}{2},\frac{3\pi}{4},\pi]

Choose the correct answer Which of the following is a necessary condition for a function

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f(x)

to be continuous at

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x=a

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f(x)

must be differentiable at

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x=a

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\lim_{x \to a}f(x)=f(a)

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f(a)=0

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f(x)

must have a positive slope at

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x=a

Find the values of

x,y,z

based on the equations:

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\ x(z+1)=y^{2}

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\((z+1)^{2}=xy\)

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\ x^{2}=y(z+1)

Verify that with

\sigma=(1\,2)

\tau=(1\,2\,3)

, the standard representation has a basis

\alpha=(\omega,1,\omega^{2})

\beta=(1,\omega,\omega^{2})

\tau \alpha=\omega \alpha

\tau \beta=\omega^{2}\beta

\sigma \alpha=\beta

\sigma \beta=\alpha

For what value of

k

is the function

f(x)=\begin{cases} \frac{\sin x+x\cos x}{x}, & x\neq 0, \ 3k, & x=0 \end{cases}

is continuous at

x=0

What is the midline equation of

y=7\sin\left(\frac{3\pi}{4}x-\frac{\pi}{4}\right)+6

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y

Find the derivative of the function.

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s(x) = x(x^2 - \frac{3}{x})

s'(x) = ?

Dew point temperature, in degrees Celsius (

^\circ C

), is defined as the temperature to which the air would have to cool in order to reach saturation. For a temperature of

35^\circ C

, an estimate of the dew point can be obtained by first subtracting

20^\circ C

from the temperature, and then adding

1^\circ

for every increase of

5

points in the relative humidity,

R

. If the dew point is

30^\circ C

, which of the following equations best models the situation?

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1

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30=15-\frac{1}{5}R

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30=15+5R

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30=15-5R

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30=15+\frac{1}{5}R

Solve the given equation system

x(z+1)=y^{2}, \ (z+1)^{2}=xy, \ x^{2}=y(z+1)

Find the reference angle for a rotation of

\frac{3 \pi}{11}

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Find the radius of the circle.

x^{2}+y^{2}=36

26

5

\cos ^{2}(2 x)-2 \cos (2 x)=-1

[0,2 \pi]

y

-coordinate of the

y

-intercept of the polynomial function defined below.

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f(x)=-x^{3}-8 x+3-4 x^{4}+2 x^{2}

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y

-coordinate of the

y

-intercept of the polynomial function defined below.

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f(x)=5 x^{3}+x^{2}-2+6 x

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y

-coordinate of the

y

-intercept of the polynomial function defined below.

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f(x)=7 x^{2}-6 x+2 x^{4}+3 x^{3}

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y

-coordinate of the

y

-intercept of the polynomial function defined below.

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f(x)=-2 x^{2}-5 x+2 x^{3}-3

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y

-coordinate of the

y

-intercept of the polynomial function defined below.

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

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y

-coordinate of the

y

-intercept of the polynomial function defined below.

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f(x)=-8 x^{3}-5+8 x+2 x^{2}

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y

-coordinate of the

y

-intercept of the polynomial function defined below.

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

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y

-coordinate of the

y

-intercept of the polynomial function defined below.

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f(x)=5 x^{3}-7 x-1-6 x^{2}

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In a lab experiment, a population of

400

bacteria is able to triple every hour. Which equation matches the number of bacteria in the population after

2

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B=400(3)(3)

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B=400(3)(3)(3)

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B=3(1+400)^{2}

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B=3(400)^{2}

Three points on the graph of the function

f(x)

\{(0,1),(1,2),(2,5)\}

. Which equation represents

f(x)

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

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f(x)=2^{x}

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f(x)=x+1

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f(x)=3 x-1

Three points on the graph of the function

f(x)

\{(0,1),(1,2),(2,4)\}

. Which equation represents

f(x)

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

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f(x)=2^{x}

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f(x)=2 x

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f(x)=x+1

Three points on the graph of the function

f(x)

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

. Which equation represents

f(x)

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f(x)=x^{2}+2

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f(x)=x-2

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f(x)=2 \cdot\left(\frac{3}{2}\right)^{x}

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f(x)=x+2

Three points on the graph of the function

f(x)

\{(0,1),(1,2),(2,4)\}

. Which equation represents

f(x)

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

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f(x)=2 x

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f(x)=2^{x}

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f(x)=x+1

Three points on the graph of the function

f(x)

\{(0,2),(1,4),(2,6)\}

. Which equation represents

f(x)

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f(x)=2 \cdot 2^{x}

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f(x)=2 x+2

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f(x)=\frac{1}{2} x-1

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f(x)=x^{2}+2

Three points on the graph of the function

f(x)

\{(0,1),(1,2),(2,5)\}

. Which equation represents

f(x)

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

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f(x)=2^{x}

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f(x)=3 x-1

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f(x)=x+1

Three points on the graph of the function

f(x)

\{(0,2),(1,4),(2,8)\}

. Which equation represents

f(x)

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f(x)=x^{2}+2

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f(x)=2(2)^{x}

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f(x)=2 x+2

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f(x)=4 x

Three points on the graph of the function

f(x)

\{(0,1),(1,2),(2,5)\}

. Which equation represents

f(x)

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f(x)=2^{x}

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f(x)=3 x-1

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

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f(x)=x+1

What is the midline equation of the function

h(x)=-3\cos(\pi x+2)-6

The derivative of the function

f

f^{\prime}(x)=x^{2}+5 \sin (2 x+5)

-2.5<x<3

. Find all intervals in the given domain where the function

f

is decreasing. You may use a calculator and round all values to

3

decimal places.

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What is the midline equation of the function

h(x)=-4\cos(5x-9)-7?

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y = \square

What is the period of

y=3\cos(x-7)+2

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Give an exact value.

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1

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2\pi

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\pi

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\frac{2\pi}{3}

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\frac{\pi}{2}

h'(1)

h(x)=f(\sqrt{g(2-x^{2})})

g(1)=4

f'(2)=2

Adam is preheating his oven before using it to bake. Adam wants to predict the final temperature after

x

minutes. He wrote the equation

y=25 x+80

y

represents the final temperature in degrees Fahrenheit. What could the number

80

in Adam's equation represent?

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The time when the oven's temperature is

0^{\circ}

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The change in minutes for every change of one degree Fahrenheit.

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The temperature the oven starts at.

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The change in degrees Fahrenheit for every change of one minute.

For the following equation, what is the instantaneous rate of change at

x=1

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f(x)=-2 x^{5}+2 x^{2}-5

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Complete the recursive formula of the arithmetic sequence

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20,26,32,38,\dots

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a(1)=\square

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a(n) = a(n-1) +6

The highest recorded wind speed not associated with a tornado was recorded at Barrows Island, Australia, in the year

1996

. The wind gust of

220 \text{ knots}

(\text{kn})

toppled the previous record held at Mount Washington. What was the wind speed in miles per hour

\left(\frac{\text{mi}}{\text{hr}}\right)

\left[1\text{kn}=1.15\left(\frac{\text{mi}}{\text{hr}}\right)\right]

What is the midline equation of the function

g(x)=-6\sin(3\pi x+4)-2

y=\square

What is the midline equation of

y=2\sin\left(\frac{\pi}{2}x+3\right)

y=\square

What is the midline equation of the function

g(x)=-\sin(8x-3)+5

y=\Box

f(x)=-3 \cot ^{2}(x)

f^{\prime}(x)

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f^{\prime}(x)=

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f

g

f(x)=x-2

g(x)=\sqrt{x+3}

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a) Find the domain of

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f

g

f+g

f-g

fg

f^2

g

0

g

1

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g

2

g

3

g

4

g

5

g

6

g

7

What is the period of

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y=3\cos(x-7)+2

? Give an exact value.

\frac{dy}{dx}

\frac{d^2y}{dx^2}

x=1+t^2\quad y=t-t^3

Determine whether the function

f(x)

is continuous at

x=3

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f(x)=\left\{\begin{array}{ll} 10-3 x^{2}, & x>3 \\ -9-3 x, & x \leq 3 \end{array}\right.

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f(x)

is discontinuous at

x=3

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f(x)

is continuous at

x=3

Determine whether the function

f(x)

is continuous at

x=3

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f(x)=\left\{\begin{array}{ll} 4-3 x^{2}, & x>3 \\ -13-3 x, & x \leq 3 \end{array}\right.

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f(x)

is discontinuous at

x=3

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f(x)

is continuous at

x=3

...