Question 1

Find the limit.

Accepted Answer

B

Question 2

The integrals  and  are called Fresnel integrals. They are used to explain the phenomenon of light diffraction.Evaluate the given limit.

Accepted Answer

1/6

Question 3

Find the given integral.

Accepted Answer

The answer of Find the given integral. ...

Question 4

Find the limit.

Accepted Answer

The answer of Find the limit. 
...

Question 5

At what point of the curve  does the tangent line have slope  ?

Accepted Answer

The answer of At what point of the curve ...

Question 6

A painting in an art gallery has height h and is hung so that lower edge is a distance d above the eye of an observer (as in the figure). How far from the wall should the observer stand to get the best view? (In other words, where should the observer stand so as to maximize the angle  subtended at his eye by the painting?)

Accepted Answer

The answer of A painting in an art gallery has...

Question 7

Find the value of the expression accurate to four decimal places. cosh 2

Accepted Answer

The answer of Find the value of the expression accurate...

Question 8

Evaluate the limit using l'Hôpital's Rule.

Accepted Answer

The answer of Evaluate the limit using l'Hôpital's Rule. 
...

Question 9

Find the derivative of the function. f(x) = sinh 4x

Accepted Answer

Using the chain rule, we have:
f'(x) = cosh(4x) * 4
= 4cosh(4x)

Question 10

Find the derivative of the function. f (x) = sinh ^-¹ 6x

Accepted Answer

The answer of Find the derivative of the function.
f (x)...

Question 11

Use the definitions of the hyperbolic functions to find the following limit.

Accepted Answer

The answer of Use the definitions of the hyperbolic functions...

Question 12

A telephone line hangs between two poles at 12 m apart in the shape of the catenary  , where x and y are measured in meters. Find the slope of this curve where it meets the right pole.

Accepted Answer

The answer of A telephone line hangs between two poles...

Question 13

Find the limit  , if it exists.

Accepted Answer

The answer of Find the limit  , if it...

Question 14

Use l'Hospital's Rule to calculate the exact value of the limit as

Accepted Answer

The answer of Use l'Hospital's Rule to calculate the exact...

Question 15

Find the derivative of the function.

Accepted Answer

The answer of Find the derivative of the function. 
...

Question 16

Find the derivative of the function. f (t) = cosh²(6t² + 3)

Accepted Answer

The derivative of cosh^2(u) is 2*cosh(u)*sinh(u)*u', where u = 6t^2 + 3 and u' = 12t. Thus, the derivative is 2*cosh(6t^2 + 3)*sinh(6t^2 + 3)*12t = 24t*cosh(6t^2 + 3)*sinh(6t^2 + 3).

Question 17

Find the given integral.

Accepted Answer

The given integral is of the form e^ax where a = 9 and hence the antiderivative will be of the form (1/a)e^ax + C. Substituting the value of a, we get (1/9)e^(9x) + C. But as there is an additional sinh(9x+5), the final antiderivative will be (1/9)e^(9x)sinh(9x+5) + C, which matches with option C.

Question 18

Find the derivative of y.

Accepted Answer

The answer of Find the derivative of y. 
...

Question 19

Find the limit  , if it exists.

Accepted Answer

The answer of Find the limit  , if it...

Question 20

Find the derivative of the function. y =

Accepted Answer

This is a complex number in exponential form, where the real part is 11 and the imaginary part is given by the rest of the expression. To find the derivative, we simply take the derivative of the imaginary part with respect to the variable being differentiated. In this case, there are no variables explicitly stated, so we assume it is with respect to the standard variable, which is usually x. However, since the variable is not explicitly stated, we can ignore it for the purposes of differentiation and treat the imaginary part as a constant.

The derivative of any constant is 0, so the derivative of this complex number is just the derivative of the real part, which is 0.

Therefore, the answer is D) 11eaa3e5_5553_e153_9f8f_65d44a8f3e9c_TB5971_11.

Quiz 6: Inverse Functions

Find the limit.

The integrals and are called Fresnel integrals. They are used to explain the phenomenon of light diffraction.Evaluate the given limit.

Find the given integral.

Find the limit.

At what point of the curve does the tangent line have slope ?

Find the value of the expression accurate to four decimal places. cosh 2

Evaluate the limit using l'Hôpital's Rule.

Find the derivative of the function. f(x) = sinh 4x

Find the derivative of the function. f (x) = sinh -1 6x

Use the definitions of the hyperbolic functions to find the following limit.

A telephone line hangs between two poles at 12 m apart in the shape of the catenary , where x and y are measured in meters. Find the slope of this curve where it meets the right pole.

Find the limit , if it exists.

Use l'Hospital's Rule to calculate the exact value of the limit as

Find the derivative of the function.

Find the derivative of the function. f (t) = cosh2(6t2 + 3)

Find the given integral.

Find the derivative of y.

Find the limit , if it exists.

Find the derivative of the function. y =

Find the derivative of the function. f (x) = sinh ^-¹ 6x

Find the derivative of the function. f (t) = cosh²(6t² + 3)