Question 1

Find an equation of the line tangent to the graph of y = 6x + 4 at the point (0, 5).

Accepted Answer

A) y = (ln 6)x + 4 
B) y = 6x + 5 
C) y = 6x + 4 
D) y = (ln 6)x + 5 
A) y = (ln 6)x + 4 
B) y = 6x + 5 
C) y = 6x + 4 
D) y = (ln 6)x + 5

Question 2

Find the limit   , if it exists.

Accepted Answer

The answer of Find the limit   , if...

Question 3

Differentiate the function.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 4

Find the given integral.

Accepted Answer

A) 9sinh (9x + 5) + C 
B) sinh (9x + 5)+ C 
C)    sinh (9x + 5) + C 
D) -sinh (9x + 5)+ C 
A) 9sinh (9x + 5) + C 
B) sinh (9x + 5)+ C 
C)    sinh (9x + 5) + C 
D) -sinh (9x + 5)+ C

Question 5

Solve the equation. 2e x + 5 = 4

Accepted Answer

A) x = ln   - 5 
B) x = ln   + 5 
C) x = ln   + 5 
D) x = ln   - 5 
A) x = ln   - 5 
B) x = ln   + 5 
C) x = ln   + 5 
D) x = ln   - 5

Question 6

Use the graph of y = ln x as an aid to sketch the graph of the function.
g(x) = ln(x + 1)

Accepted Answer

The answer of Use the graph of y = ln...

Question 7

Differentiate the function.

Accepted Answer

The answer of Differentiate the function.  ...

Question 8

Find the inverse function.

Accepted Answer

The answer of Find the inverse function.  ...

Question 9

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

Accepted Answer

A) 12t cosh (6t2 + 3) sinh (6t2 + 3) 
B) 24t sinh (6t2 + 3) 
C) 24t cosh (6t2 + 3) sinh (6t2 + 3) 
D) 12t sinh (6t2 + 3) 
A) 12t cosh (6t2 + 3) sinh (6t2 + 3) 
B) 24t sinh (6t2 + 3) 
C) 24t cosh (6t2 + 3) sinh (6t2 + 3) 
D) 12t sinh (6t2 + 3)

Question 10

Find the limit.

Accepted Answer

A) 5 
B)    
C) 0 
D)    
E)    
A) 5 
B)    
C) 0 
D)    
E)

Question 11

Use the properties of logarithms to expand the quantity.

Accepted Answer

The answer of Use the properties of logarithms to expand...

Question 12

Differentiate the function. y = x(72x)

Accepted Answer

A) [1 + (2 ln 7)x]72x 
B) [1 + (7 ln 2)x]72x 
C) (2 ln 7)72x 
D) (2 ln 7)(72x)x 
A) [1 + (2 ln 7)x]72x 
B) [1 + (7 ln 2)x]72x 
C) (2 ln 7)72x 
D) (2 ln 7)(72x)x

Question 13

Find the limit.

Accepted Answer

A)    
B)    
C)    
D) 1 
E) 0 
A)    
B)    
C)    
D) 1 
E) 0

Question 14

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

Accepted Answer

A) 3.3811 
B) 5.6269 
C) 8.5244 
D) 3.7622 
A) 3.3811 
B) 5.6269 
C) 8.5244 
D) 3.7622

Question 15

A lighthouse is located on a small island,   km away from the nearest point P on a straight shoreline, and its light makes four revolutions per minute. How fast is the beam of light moving along the shoreline when it is 1 km from P?

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 16

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

Accepted Answer

A)    
B)    
C)    
D)    
E) 0 
A)    
B)    
C)    
D)    
E) 0

Question 17

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

Accepted Answer

The answer of The integrals   and  ...

Question 18

Evaluate the integral.

Accepted Answer

The answer of Evaluate the integral.  ...

Question 19

Solve the inequality.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 20

Find the solution of the equation correct to four decimal places.

Accepted Answer

The answer of Find the solution of the equation correct...

Find an equation of the line tangent to the graph of y = 6^x+ 4 at the point (0, 5).

Find the limit , if it exists.

Differentiate the function.

Find the given integral.

Solve the equation. 2e ^x^{+ 5}= 4

Use the graph of y = ln x as an aid to sketch the graph of the function. g(x) = ln(x + 1)

Differentiate the function.

Find the inverse function.

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

Find the limit.

Use the properties of logarithms to expand the quantity.

Differentiate the function. y = x(7²^x)

Find the limit.

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

A lighthouse is located on a small island, km away from the nearest point P on a straight shoreline, and its light makes four revolutions per minute. How fast is the beam of light moving along the shoreline when it is 1 km from P?

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

Evaluate the integral.

Solve the inequality.

Find the solution of the equation correct to four decimal places.

Functions and Limits

Derivatives

Applications of Differentiation

Integrals

Applications of Integration

Techniques of Integration

Further Applications of Integration

Differential Equations

Parametric Equations and Polar Coordinates

Infinite Sequences and Series

Vectors and the Geometry of Space

Vector Functions

Partial Derivatives

Multiple Integrals

Vector Calculus

Second-Order Differential Equations

Final Exam

Filters

Exam 6: Inverse Functions

Find an equation of the line tangent to the graph of y = 6x + 4 at the point (0, 5).

Find the limit , if it exists.

Differentiate the function.

Find the given integral.

Solve the equation. 2e x + 5 = 4

Use the graph of y = ln x as an aid to sketch the graph of the function. g(x) = ln(x + 1)

Differentiate the function.

Find the inverse function.

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

Find the limit.

Use the properties of logarithms to expand the quantity.

Differentiate the function. y = x(72x)

Find the limit.

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

A lighthouse is located on a small island, km away from the nearest point P on a straight shoreline, and its light makes four revolutions per minute. How fast is the beam of light moving along the shoreline when it is 1 km from P?

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

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

Evaluate the integral.

Solve the inequality.

Find the solution of the equation correct to four decimal places.

Functions and Limits

Derivatives

Applications of Differentiation

Integrals

Applications of Integration

Techniques of Integration

Further Applications of Integration

Differential Equations

Parametric Equations and Polar Coordinates

Infinite Sequences and Series

Vectors and the Geometry of Space

Vector Functions

Partial Derivatives

Multiple Integrals

Vector Calculus

Second-Order Differential Equations

Final Exam

Filters

Find an equation of the line tangent to the graph of y = 6^x+ 4 at the point (0, 5).

Solve the equation. 2e ^x^{+ 5}= 4

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

Differentiate the function. y = x(7²^x)