Question 1

For the problems below, find each limit.
- $\lim _{x \rightarrow \infty}\left(3 x^{2}-2 x\right)$

Accepted Answer

8

Question 2

Given $y=4 x^{5}-3 x^{4}+8 x^{2}$, find the first three derivatives of $y$.

Accepted Answer

$y^{\prime}=20 x^{4}-12 x^{3}+16 x, y^{\prime \prime}=80 x^{3}-36 x^{2}+16, y^{\prime \prime \prime}=240 x^{2}-72 x$

Question 3

For the problems below, find the derivative of each function.
- $y=2 x^{4}-3 x^{2}+7$

Accepted Answer

$y^{\prime}=8 x^{3}-6 x$

Question 4

Find the derivative of $y=\frac{4}{3} x^{2}-9 x^{2}+x-15$.

Accepted Answer

A)  $\frac{d y}{d x}=\frac{-72}{x^{6}}$ 
B)  $\frac{d y}{d x}=4 x^{3}-18 x^{2}+x$ 
C)  $\frac{d y}{d x}=8 x-18$ 
D)  $\frac{d y}{d x}=4 x^{2}-18 x+1$ 
A)  $\frac{d y}{d x}=\frac{-72}{x^{6}}$ 
B)  $\frac{d y}{d x}=4 x^{3}-18 x^{2}+x$ 
C)  $\frac{d y}{d x}=8 x-18$ 
D)  $\frac{d y}{d x}=4 x^{2}-18 x+1$

Question 5

For the problems below, find each limit.
-  $\lim _{\mathrm{x} \rightarrow} \frac{4 \mathrm{x}^{2}-7}{8 \mathrm{x}^{2}+5}$

Accepted Answer

The answer of For the problems below, find each limit.
-...

Question 6

Find the derivative of $y=\frac{1}{3 x-4}$.

Accepted Answer

A)  $\frac{d y}{d x}=\frac{-1}{(3 x-4)^{3}}$ 
B)  $\frac{d y}{d x}=3$ 
C)  $\frac{d y}{d x}=\frac{-3}{(3 x-4)^{2}}$ 
D)  $\frac{d y}{d x}=\frac{3}{3 x-4}$ 
A)  $\frac{d y}{d x}=\frac{-1}{(3 x-4)^{3}}$ 
B)  $\frac{d y}{d x}=3$ 
C)  $\frac{d y}{d x}=\frac{-3}{(3 x-4)^{2}}$ 
D)  $\frac{d y}{d x}=\frac{3}{3 x-4}$

Question 7

Find the derivative of $y=\frac{4 x-8}{8 x+15}$.

Accepted Answer

A)  $\frac{d y}{d x}=\frac{64 x-4}{(8 x+15)^{2}}$ 
B)  $\frac{d y}{d x}=\frac{124}{64 x^{2}+255}$ 
C)  $\frac{d y}{d x}=\frac{124}{(8 x+15)^{2}}$ 
D)  $\frac{\mathrm{dy}}{\mathrm{dx}}=\frac{1}{2}$ 
A)  $\frac{d y}{d x}=\frac{64 x-4}{(8 x+15)^{2}}$ 
B)  $\frac{d y}{d x}=\frac{124}{64 x^{2}+255}$ 
C)  $\frac{d y}{d x}=\frac{124}{(8 x+15)^{2}}$ 
D)  $\frac{\mathrm{dy}}{\mathrm{dx}}=\frac{1}{2}$

Question 8

For the problems below, find the derivative of each function.
-$y=2 x^{2}-5 x$

Accepted Answer

The answer of For the problems below, find the derivative...

Question 9

Find the equation of the line tangent to the curve $y=3 x^{2}-9$ at (4, 39).

Accepted Answer

The answer of Find the equation of the line tangent...

Question 10

For the problems below, find the derivative using implicit differentiation.
-  $y=3 x y^{2}+\sqrt{x-1}$

Accepted Answer

The answer of For the problems below, find the derivative...

Question 11

Find the derivative of $y=\frac{1}{\left(4 x^{3}-6 x+8\right)^{2}}$.

Accepted Answer

A)  $\frac{d y}{d x}=\frac{12 x^{2}-6}{\left(4 x^{3}-6 x+8\right)^{3}}$ 
B)  $\frac{d y}{d x}=\frac{-12\left(2 x^{2}-1\right)}{\left(4 x^{3}-6 x+8\right)^{4}}$ 
C)  $\frac{d y}{d x}=\frac{12 x^{2}-6}{\left(4 x^{3}-6 x+8\right)^{4}}$ 
D)  $\frac{d y}{d x}=\frac{-12\left(2 x^{2}-1\right)}{\left(4 x^{3}-6 x+8\right)^{3}}$ 
A)  $\frac{d y}{d x}=\frac{12 x^{2}-6}{\left(4 x^{3}-6 x+8\right)^{3}}$ 
B)  $\frac{d y}{d x}=\frac{-12\left(2 x^{2}-1\right)}{\left(4 x^{3}-6 x+8\right)^{4}}$ 
C)  $\frac{d y}{d x}=\frac{12 x^{2}-6}{\left(4 x^{3}-6 x+8\right)^{4}}$ 
D)  $\frac{d y}{d x}=\frac{-12\left(2 x^{2}-1\right)}{\left(4 x^{3}-6 x+8\right)^{3}}$

Question 12

Find the second derivative of $y=y^{2}-3 x^{4}+4$.

Accepted Answer

A)  $y^{\prime \prime}=\frac{72 x^{2} y-36 x^{2}-288 x^{6}}{(1-2 y)^{3}}$ 
B)  $y^{\prime \prime}=\frac{\left(72 x^{2} y-36 x^{2}\right)(1-2 y)-288 x^{6}}{(1-2 y)^{2}}$ 
C)  $y^{\prime \prime}=\frac{(1-2 y)\left(36 x^{2} y-18 x^{2}\right)}{(1-2 y)^{3}}$ 
D)  $y^{\prime \prime}=\frac{\left(72 x^{2} y-36 x^{2}\right)(1-2 y)-288 x^{6}}{(1-2 y)^{3}}$ 
A)  $y^{\prime \prime}=\frac{72 x^{2} y-36 x^{2}-288 x^{6}}{(1-2 y)^{3}}$ 
B)  $y^{\prime \prime}=\frac{\left(72 x^{2} y-36 x^{2}\right)(1-2 y)-288 x^{6}}{(1-2 y)^{2}}$ 
C)  $y^{\prime \prime}=\frac{(1-2 y)\left(36 x^{2} y-18 x^{2}\right)}{(1-2 y)^{3}}$ 
D)  $y^{\prime \prime}=\frac{\left(72 x^{2} y-36 x^{2}\right)(1-2 y)-288 x^{6}}{(1-2 y)^{3}}$

Question 13

For the problems below, evaluate each function at the given value.
-19 $f(t)=2 t^{3}+t-6 ; t=4$

Accepted Answer

The answer of For the problems below, evaluate each function...

Question 14

Find the slope of the line tangent to the curve $y=x^{2}-4 x+7$ at $(5,12)$.

Accepted Answer

The answer of Find the slope of the line tangent...

Question 15

For the problems below, find the derivative of each function.
- $y=x^{8}\left(3 x^{2}+5 x-7\right)$

Accepted Answer

The answer of For the problems below, find the derivative...

Question 16

For the problems below, find: a) $\Delta \mathrm{s}$ and b) $\overline{\mathrm{v}}$ for each function expressing distance $\mathrm{s}$ in terms of time $\mathrm{t}$. 21) $s=5 t+3$
-Given $s=f(t)=4 t^{2}$ - 9, find the instantaneous velocity $v$ of an object moving along a straight line when $t=3$. The distance, $s$, is in metres and $t$ is in seconds.

Accepted Answer

The answer of For the problems below, find: a) \(\Delta...

Question 17

Find the slope of the line tangent to $y=4 x^{2}-5 x+6$ at the point (-2, 32).

Accepted Answer

A)  11 
B)  8 
C)  - 21 
D)  - 11 
A)  11 
B)  8 
C)  - 21 
D)  - 11

Question 18

For the problems below, find the derivative of each function.
- $y=\frac{(4 x-1)^{6}}{(3 x+2)^{4}}$

Accepted Answer

The answer of For the problems below, find the derivative...

Question 19

Find $\lim _{x \rightarrow} \frac{8 x-3}{x}$.

Accepted Answer

A)  5 
B)  -3 
C)  8 
D)  0 
A)  5 
B)  -3 
C)  8 
D)  0

Question 20

For the problems below, find each limit.
-  $\lim _{\mathrm{x} \rightarrow 8} 5$

Accepted Answer

The answer of For the problems below, find each limit.
-...

For the problems below, find each limit. - $\lim _{x \rightarrow \infty}\left(3 x^{2}-2 x\right)$

Given $y=4 x^{5}-3 x^{4}+8 x^{2}$ , find the first three derivatives of $y$ .

For the problems below, find the derivative of each function. - $y=2 x^{4}-3 x^{2}+7$

Find the derivative of $y=\frac{4}{3} x^{2}-9 x^{2}+x-15$ .

For the problems below, find each limit. - $\lim _{\mathrm{x} \rightarrow} \frac{4 \mathrm{x}^{2}-7}{8 \mathrm{x}^{2}+5}$

Find the derivative of $y=\frac{1}{3 x-4}$ .

Find the derivative of $y=\frac{4 x-8}{8 x+15}$ .

For the problems below, find the derivative of each function. - $y=2 x^{2}-5 x$

Find the equation of the line tangent to the curve $y=3 x^{2}-9$ at (4, 39).

For the problems below, find the derivative using implicit differentiation. - $y=3 x y^{2}+\sqrt{x-1}$

Find the derivative of $y=\frac{1}{\left(4 x^{3}-6 x+8\right)^{2}}$ .

Find the second derivative of $y=y^{2}-3 x^{4}+4$ .

For the problems below, evaluate each function at the given value. -19 $f(t)=2 t^{3}+t-6 ; t=4$

Find the slope of the line tangent to the curve $y=x^{2}-4 x+7$ at $(5,12)$ .

For the problems below, find the derivative of each function. - $y=x^{8}\left(3 x^{2}+5 x-7\right)$

Find the slope of the line tangent to $y=4 x^{2}-5 x+6$ at the point (-2, 32).

For the problems below, find the derivative of each function. - $y=\frac{(4 x-1)^{6}}{(3 x+2)^{4}}$

Find $\lim _{x \rightarrow} \frac{8 x-3}{x}$ .

For the problems below, find each limit. - $\lim _{\mathrm{x} \rightarrow 8} 5$

Analytic Geometry

Applications of the Derivative

Derivatives of Transcendental Functions

The Integral

Applications of Integration

Methods of Integration

Three-Space: Partial Derivatives and Double Integrals

Progressions and the Binomial Theorem

Series

First-Order Differential Equations

Second-Order Differential Equations

Filters

Exam 2: The Derivative

For the problems below, find each limit. - lim⁡x→∞(3x2−2x)\lim _{x \rightarrow \infty}\left(3 x^{2}-2 x\right)limx→∞​(3x2−2x)

Given y=4x5−3x4+8x2y=4 x^{5}-3 x^{4}+8 x^{2}y=4x5−3x4+8x2 , find the first three derivatives of yyy .

For the problems below, find the derivative of each function. - y=2x4−3x2+7y=2 x^{4}-3 x^{2}+7y=2x4−3x2+7

Find the derivative of y=43x2−9x2+x−15y=\frac{4}{3} x^{2}-9 x^{2}+x-15y=34​x2−9x2+x−15 .

For the problems below, find each limit. - lim⁡x→4x2−78x2+5\lim _{\mathrm{x} \rightarrow} \frac{4 \mathrm{x}^{2}-7}{8 \mathrm{x}^{2}+5}limx→​8x2+54x2−7​

Find the derivative of y=13x−4y=\frac{1}{3 x-4}y=3x−41​ .

Find the derivative of y=4x−88x+15y=\frac{4 x-8}{8 x+15}y=8x+154x−8​ .

For the problems below, find the derivative of each function. - y=2x2−5xy=2 x^{2}-5 xy=2x2−5x

Find the equation of the line tangent to the curve y=3x2−9y=3 x^{2}-9y=3x2−9 at (4, 39).

For the problems below, find the derivative using implicit differentiation. - y=3xy2+x−1y=3 x y^{2}+\sqrt{x-1}y=3xy2+x−1​

Find the derivative of y=1(4x3−6x+8)2y=\frac{1}{\left(4 x^{3}-6 x+8\right)^{2}}y=(4x3−6x+8)21​ .

Find the second derivative of y=y2−3x4+4y=y^{2}-3 x^{4}+4y=y2−3x4+4 .

For the problems below, evaluate each function at the given value. -19 f(t)=2t3+t−6;t=4f(t)=2 t^{3}+t-6 ; t=4f(t)=2t3+t−6;t=4

Find the slope of the line tangent to the curve y=x2−4x+7y=x^{2}-4 x+7y=x2−4x+7 at (5,12)(5,12)(5,12) .

For the problems below, find the derivative of each function. - y=x8(3x2+5x−7)y=x^{8}\left(3 x^{2}+5 x-7\right)y=x8(3x2+5x−7)

Find the slope of the line tangent to y=4x2−5x+6y=4 x^{2}-5 x+6y=4x2−5x+6 at the point (-2, 32).

For the problems below, find the derivative of each function. - y=(4x−1)6(3x+2)4y=\frac{(4 x-1)^{6}}{(3 x+2)^{4}}y=(3x+2)4(4x−1)6​

Find lim⁡x→8x−3x\lim _{x \rightarrow} \frac{8 x-3}{x}limx→​x8x−3​ .

For the problems below, find each limit. - lim⁡x→85\lim _{\mathrm{x} \rightarrow 8} 5limx→8​5

Analytic Geometry

Applications of the Derivative

Derivatives of Transcendental Functions

The Integral

Applications of Integration

Methods of Integration

Three-Space: Partial Derivatives and Double Integrals

Progressions and the Binomial Theorem

Series

First-Order Differential Equations

Second-Order Differential Equations

Filters

For the problems below, find each limit. - $\lim _{x \rightarrow \infty}\left(3 x^{2}-2 x\right)$

Given $y=4 x^{5}-3 x^{4}+8 x^{2}$ , find the first three derivatives of $y$ .

For the problems below, find the derivative of each function. - $y=2 x^{4}-3 x^{2}+7$

Find the derivative of $y=\frac{4}{3} x^{2}-9 x^{2}+x-15$ .

For the problems below, find each limit. - $\lim _{\mathrm{x} \rightarrow} \frac{4 \mathrm{x}^{2}-7}{8 \mathrm{x}^{2}+5}$

Find the derivative of $y=\frac{1}{3 x-4}$ .

Find the derivative of $y=\frac{4 x-8}{8 x+15}$ .

For the problems below, find the derivative of each function. - $y=2 x^{2}-5 x$

Find the equation of the line tangent to the curve $y=3 x^{2}-9$ at (4, 39).

For the problems below, find the derivative using implicit differentiation. - $y=3 x y^{2}+\sqrt{x-1}$

Find the derivative of $y=\frac{1}{\left(4 x^{3}-6 x+8\right)^{2}}$ .

Find the second derivative of $y=y^{2}-3 x^{4}+4$ .

For the problems below, evaluate each function at the given value. -19 $f(t)=2 t^{3}+t-6 ; t=4$

Find the slope of the line tangent to the curve $y=x^{2}-4 x+7$ at $(5,12)$ .

For the problems below, find the derivative of each function. - $y=x^{8}\left(3 x^{2}+5 x-7\right)$

Find the slope of the line tangent to $y=4 x^{2}-5 x+6$ at the point (-2, 32).

For the problems below, find the derivative of each function. - $y=\frac{(4 x-1)^{6}}{(3 x+2)^{4}}$

Find $\lim _{x \rightarrow} \frac{8 x-3}{x}$ .

For the problems below, find each limit. - $\lim _{\mathrm{x} \rightarrow 8} 5$