Question 1

Using the position function  , find the acceleration function.

Accepted Answer

The acceleration function can be found by taking the second derivative of the position function. 
The position function is given by:
y(t) = 11e^(-0.2t)sin(5t)

Taking the derivative once gives the velocity function:
v(t) = y'(t) = -2.2e^(-0.2t)sin(5t) + 5e^(-0.2t)cos(5t)

Taking the derivative again gives the acceleration function:
a(t) = v'(t) = -4.4e^(-0.2t)cos(5t) - 5e^(-0.2t)sin(5t) - 1e^(-0.2t)sin(5t) - 25e^(-0.2t)cos(5t)

Simplifying this expression, we get:
a(t) = (11e^(-0.2t))(-4.4cos(5t) - 26sin(5t))

Therefore, the answer is C: 11eaa88b_9250_553e_a696_836b36260498_TB5869_11.

Question 2

Find the derivative of  .

Accepted Answer

The answer of Find the derivative of  .
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Question 3

Differentiate the function.

Accepted Answer

The answer of Differentiate the function. 
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Question 4

Below is a graph of  . Sketch a plausible graph of a continuous function  .

Accepted Answer

The answer of Below is a graph of  ....

Question 5

Find the derivative of f(x) = -5x² + 2x - 5.

Accepted Answer

The derivative of f(x) = -5x^2 + 2x - 5 is found by applying the power rule: the derivative of -5x^2 is -10x, the derivative of 2x is 2, and the derivative of a constant (-5) is 0. Therefore, the derivative is -10x + 2.

Question 6

Find the second derivative of  .

Accepted Answer

The answer of Find the second derivative of  .
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Question 7

Give the units for the derivative function.  represents the amount of a chemical present, in milligrams, at time t seconds.

Accepted Answer

The answer of Give the units for the derivative function....

Question 8

Suppose a sprinter reaches the following distances in the given times. Estimate the velocity of the sprinter at the 6 second mark. Round to the nearest integer. t sec
5
5)5
6
6)5
7  ft
121)7
142)5
158)5
174)7
193)9

Accepted Answer

The answer of Suppose a sprinter reaches the following distances...

Question 9

Find the derivative of  .

Accepted Answer

The answer of Find the derivative of  .
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Question 10

Sketch the graph of a function with the following properties:      and

Accepted Answer

The answer of Sketch the graph of a function with...

Question 11

Find the third derivative of  .

Accepted Answer

The third derivative of any term of the form $ax^n$ is $a\cdot n(n-1)(n-2)x^{n-3}$.
In this case, $a=11$, $n=eaa88b_{16}$ (which is a hexadecimal representation of a number), and $x=TB5869_{16}$ (which is also a hexadecimal representation of a number). 
Converting $n$ to decimal, we get $n=15,778,891$. 
Therefore, the third derivative is $11\cdot 15,778,891 \cdot (15,778,891 -1) \cdot (15,778,891 -2) \cdot TB5869_{16}^{15,778,888}$.

Converting this derivative back to hexadecimal form, we get the answer D: 11eaa88b_924f_6ad5_a696_ff5a7119cd6f_TB5869_11.

Question 12

Differentiate the function.

Accepted Answer

The answer of Differentiate the function. 
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Question 13

Using the position function  , find the velocity function.

Accepted Answer

To find the velocity function, we need to differentiate the position function with respect to time. 
Derivative of 11eaa88b_9250_7c50_a696_a7f9871f7dff_TB5869_11 with respect to time (t) is:
11eaa88b_9250_7c50_a696_a7f9871f7dff_TB5869_11' = 2t - 5
Therefore, the velocity function is 11eaa88b_9250_ca72_a696_1d0345f61d35_TB5869_11.

Question 14

Find the derivative of  .

Accepted Answer

The answer of Find the derivative of  .
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Question 15

Differentiate the function.

Accepted Answer

The answer of Differentiate the function. 
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Question 16

Below is a graph of  . Sketch a plausible graph of a continuous function  .

Accepted Answer

The answer of Below is a graph of  ....

Question 17

Compute the right-hand derivative  and the left-hand derivative  .

Accepted Answer

The answer of Compute the right-hand derivative  and the...

Question 18

Below is a graph of  . Sketch a graph of  .

Accepted Answer

The answer of Below is a graph of  ....

Question 19

For  find all real numbers a and b such that  exists.

Accepted Answer

The answer of For  find all real numbers a...

Question 20

Using the position function  , find the velocity function.

Accepted Answer

The answer of Using the position function  , find...

Quiz 3: Differentiation

Using the position function , find the acceleration function.

Find the derivative of .

Differentiate the function.

Below is a graph of . Sketch a plausible graph of a continuous function .

Find the derivative of f(x) = -5x² + 2x - 5.

Find the second derivative of .

Give the units for the derivative function. represents the amount of a chemical present, in milligrams, at time t seconds.

Suppose a sprinter reaches the following distances in the given times. Estimate the velocity of the sprinter at the 6 second mark. Round to the nearest integer. t sec 5 5) 5 6 6) 5 7 ft 121) 7 142) 5 158) 5 174) 7 193) 9

Find the derivative of .

Sketch the graph of a function with the following properties: and

Find the third derivative of .

Differentiate the function.

Using the position function , find the velocity function.

Find the derivative of .

Differentiate the function.

Below is a graph of . Sketch a plausible graph of a continuous function .

Compute the right-hand derivative and the left-hand derivative .

Below is a graph of . Sketch a graph of .

For find all real numbers a and b such that exists.

Using the position function , find the velocity function.

Quiz 3: Differentiation

Using the position function , find the acceleration function.

Find the derivative of .

Differentiate the function.

Below is a graph of . Sketch a plausible graph of a continuous function .

Find the derivative of f(x) = -5x2 + 2x - 5.

Find the second derivative of .

Give the units for the derivative function. represents the amount of a chemical present, in milligrams, at time t seconds.

Suppose a sprinter reaches the following distances in the given times. Estimate the velocity of the sprinter at the 6 second mark. Round to the nearest integer. t sec 5 5) 5 6 6) 5 7 ft 121) 7 142) 5 158) 5 174) 7 193) 9

Find the derivative of .

Sketch the graph of a function with the following properties: and

Find the third derivative of .

Differentiate the function.

Using the position function , find the velocity function.

Find the derivative of .

Differentiate the function.

Below is a graph of . Sketch a plausible graph of a continuous function .

Compute the right-hand derivative and the left-hand derivative .

Below is a graph of . Sketch a graph of .

For find all real numbers a and b such that exists.

Using the position function , find the velocity function.

Find the derivative of f(x) = -5x² + 2x - 5.