Question 1

By using differentials,an approximation of  is
A) 
B) 
C) 
D) 
E)

Accepted Answer

Let x = 11ea83f6_636a_8516_b5a5_3db7a74eb10a_TB6578_11_TB6578_11
Taking differentials, we get:
dx ≈ f'(x) * dx = (ln(2) * 2^x) * dx
We want to find a small increment "delta" such that:
ln(2) * 2^(x + delta) * delta ≈ 1
Using trial and error, we can see that delta ≈ 0.00000001 (or 10^-8) gives us a value of approximately 1. Therefore:
x + delta ≈ 11ea83f6_636a_8519_b5a5_976ed107384b_TB6578_11_TB6578_11
Which is option C.

Question 2

Use differentials only to find an approximate value of  
.

Accepted Answer

2.9962963

Question 3

By using differentials,an approximation of ln(1.03)is
A) -0.01.
B) 0.01.
C) 0.02.
D) 0.03.
E) 0.04.

Accepted Answer

D

Question 4

If q =  
- 6  
+ 3p - 8,find  
when p = 1.

Accepted Answer

The answer of If q =  
- 6 ...

Question 5

If y =  ,then dy =
A)  dx.
B)  dx.
C) 6x  dx.
D)  dx.
E)  dx.

Accepted Answer

The last 8 digits of y (TB6578_11_TB6578_11) indicate that the number is in base 68, and the remaining digits before the underscore are in base 16. Therefore, we can ignore the TB6578_11_TB6578_11 part for our differentiation. 
The rightmost digit in the base 68 representation of y is 1, so the rightmost digit in the base 16 representation is 6. When we differentiate this digit with respect to x, we get 1. Therefore, the second rightmost digit in the base 16 representation of dy is 0+1, which gives us a 1. We can continue this process until we reach the leftmost digit, which gives us a value of 1. Thus, the correct answer is A, where the next to last hex digit is changed from b to c

Question 6

Use differentials to approximate: ln(0.95).

Accepted Answer

The answer of Use differentials to approximate: ln(0.95)....

Question 7

If y =  
,use differentials to approximate the change in y if x changes from 25 to 25.3.

Accepted Answer

The answer of If y =  
,use differentials to...

Question 8

Use differentials and R = 300x+ 50  
-  
to approximate the change in revenue R (in dollars)from selling x pounds if the number of pounds increases from 10 to 10.2.

Accepted Answer

The answer of Use differentials and R = 300x+ 50...

Question 9

If y = (  
+ 3  
,find  
.

Accepted Answer

The answer of If y = (  
+ 3...

Question 10

Find dy if y =  
.

Accepted Answer

The answer of Find dy if y =  
....

Question 11

Use differentials to approximate:  
.

Accepted Answer

The answer of Use differentials to approximate:  
....

Question 12

Find dy if y = (5  
+  
.

Accepted Answer

The answer of Find dy if y = (5 ...

Question 13

Use differentials only to find an approximate value of  
.

Accepted Answer

The answer of Use differentials only to find an approximate...

Question 14

Find the differential of the function in terms of x and dx.
y = ln(  
- 3x + 1)

Accepted Answer

The answer of Find the differential of the function in...

Question 15

Find the differential of the function in terms of x and dx.
y =

Accepted Answer

The answer of Find the differential of the function in...

Question 16

Use differentials only to find an approximate value of  
.

Accepted Answer

The answer of Use differentials only to find an approximate...

Question 17

Use differentials to approximate:

Accepted Answer

The answer of Use differentials to approximate: ...

Question 18

If y = x ln x,then dy =
A) 1 + ln x.
B) (1 + ln x) dx.
C) x + ln x.
D) (x + ln x) dx.
E) none of the above

Accepted Answer

To find the derivative of y = x ln x, we can use the product rule as follows:

y' = (ln x) dx/dx + x (1/x) = 1 + ln x

Therefore, the correct choice is B, (1 + ln x) dx.

Question 19

Use differentials only to find an approximate value of  
.

Accepted Answer

The answer of Use differentials only to find an approximate...

Question 20

Find dy if y =  
.

Accepted Answer

The answer of Find dy if y =  
....

Quiz 15: Integration

By using differentials,an approximation of is

Use differentials only to find an approximate value of .

By using differentials,an approximation of ln(1.03) is

If q = - 6 + 3p - 8,find when p = 1.

If y = ,then dy =

Use differentials to approximate: ln(0.95).

If y = ,use differentials to approximate the change in y if x changes from 25 to 25.3.

Use differentials and R = 300x+ 50 - to approximate the change in revenue R (in dollars)from selling x pounds if the number of pounds increases from 10 to 10.2.

If y = ( + 3 ,find .

Find dy if y = .

Use differentials to approximate: .

Find dy if y = (5 + .

Use differentials only to find an approximate value of .

Find the differential of the function in terms of x and dx. y = ln( - 3x + 1)

Find the differential of the function in terms of x and dx. y =

Use differentials only to find an approximate value of .

Use differentials to approximate:

If y = x ln x,then dy =

Use differentials only to find an approximate value of .

Find dy if y = .