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Let $f$ be a function such that $f(-1) = 3$ and $f'(-1) = 5$ . Let $g$ be the function $g(x) = 2x^3$ . Let $F$ be a function defined as $F(x) = \frac{f(x)}{g(x)}$

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Precalculus

Find equations of tangent lines using limits

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More problems from Find equations of tangent lines using limits

Question

The graphs of the functions

f(x)=\sin (x)

and

g(x)=\frac{1}{2}

intersect at

2

points on the interval

0<x<\pi

\newline

What is the area of the region bound by the graphs of

f(x)

and

g(x)

between those points of intersection ?

\newline

Choose

1

answer:

\newline

(A)

\frac{\pi}{3}

\newline

(B)

\frac{\pi}{2}

\newline

(C)

2-\frac{\pi}{2}

\newline

(D)

\sqrt{3}-\frac{\pi}{3}

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Posted 9 months ago

Question

What is the area of the region between the graphs of

f(x)=x^{2}+12 x

and

g(x)=3 x^{2}+10

from

x=1

x=4

\newline

Choose

1

answer:

\newline

(A)

77

\newline

(B)

\frac{64}{3}

\newline

(C)

18

\newline

(D)

45

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Posted 9 months ago

Question

What is the area of the region between the graphs of

f(x)=\sqrt{x+1}

and

g(x)=2 x-4

from

x=0

x=3

\newline

Choose

1

answer:

\newline

(A)

\frac{23}{3}

\newline

(B)

\frac{5}{3}

\newline

(C)

\frac{14}{3}

\newline

(D)

-3

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Posted 9 months ago

Question

Consider the curve given by the equation

3 x^{2}+y^{4}+6 x=253

. It can be shown that

\frac{d y}{d x}=\frac{-6(x+1)}{4 y^{3}}.

\newline

Write the equation of the horizontal line that is tangent to the curve and is above the

x

-axis.

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Posted 9 months ago

Question

The learning rate for new skills is proportional to the difference between the maximum potential for learning that skill,

M

, and the amount of the skill already learned,

L

\newline

Which equation describes this relationship?

\newline

Choose

1

answer:

\newline

(A)

L(t)=\frac{k}{(M-L)}

\newline

(B)

L(t)=k(M-L)

\newline

(C)

\frac{d L}{d t}=k(M-L)

\newline

(D)

\frac{d L}{d t}=\frac{k}{(M-L)}

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Posted 9 months ago

Question

What is the value of

\frac{d}{d x}\left(\frac{1}{x}\right)

x=6

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Posted 9 months ago

Question

What is the value of

\frac{d}{d x}(\sqrt{x})

x=9

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Posted 9 months ago

Question

A curve in the plane is defined parametrically by the equations

\newline

x=t^{3}+t

and

\newline

y=t^{4}+2t^{2}

. An equation of the line tangent to the curve at

\newline

t=1

\newline

\text{(A)}\ y=2x

\newline

\text{(B)}\ y=8x

\newline

\text{(C)}\ y=2x-1

\newline

\text{(D)}\ y=4x-5

\newline

\text{(E)}\ y=8x+13

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Posted 8 months ago

Question

A pendulum is swinging next to a wall.

\newline

The distance

D(t)

(in

\mathrm{cm}

) between the bob of the pendulum and the wall as a function of time

t

(in seconds) can be modeled by a sinusoidal expression of the form

a \cdot \sin (b \cdot t)+d

\newline

t=0

, when the pendulum is exactly in the middle of its swing, the bob is

5 \mathrm{~cm}

away from the wall. The bob reaches the closest point to the wall, which is

3 \mathrm{~cm}

from the wall,

1

second later.

\newline

Find

D(t)

\newline

t

should be in radians.

\newline

D(t)=\square

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Posted 7 months ago

Question

Pluto's distance

P(t)

(in billions of kilometers) from the sun as a function of time

t

(in years) can be modeled by a sinusoidal expression of the form

a \cdot \sin (b \cdot t)+d

\newline

At year

t=0

, Pluto is at its average distance from the sun, which is

6

9

billion kilometers. In

66

years, it is at its closest point to the sun, which is

4

4

billion kilometers away.

\newline

Find

P(t)

\newline

t

should be in radians.

\newline

P(t)=

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Posted 7 months ago

View all (7)

Let f f f be a function such that f(−1)=3 f(-1) = 3 f(−1)=3 and f′(−1)=5 f'(-1) = 5 f′(−1)=5. Let g g g be the function g(x)=2x3 g(x) = 2x^3 g(x)=2x3. Let F F F be a function defined as F(x)=f(x)g(x) F(x) = \frac{f(x)}{g(x)} F(x)=g(x)f(x)​

Let $f$ be a function such that $f(-1) = 3$ and $f'(-1) = 5$ . Let $g$ be the function $g(x) = 2x^3$ . Let $F$ be a function defined as $F(x) = \frac{f(x)}{g(x)}$