Question 1

For what value of the constant c is the function f continuous on  
A) 
B) 
C) 
D) 
E)

Accepted Answer

A

Question 2

Find the interval(s) where  is continuous.

Accepted Answer

The answer of Find the interval(s) where  is continuous....

Question 3

Determine where f is discontinuous. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

A

Question 4

Define the function  at 0 so as to make it continuous at 0.
A) 
B) 
C) 
D)

Accepted Answer

The answer of Define the function  at 0 so...

Question 5

How would you define  in order to make f continuous at  ? 
A) 
B) 
C) 
D) 
E)none of these

Accepted Answer

In order to make f continuous at 11eaa3e5_560a_3816_9f8f_e1058c2a8042_TB5971_11, the limit of f as x approaches this point from both directions needs to exist and equal the same value. Since the given function has a jump discontinuity at this point (the limit from the left is different than the limit from the right), we need to define 11eaa3e5_560a_3815_9f8f_cbf44728db31_TB5971_11 and 11eaa3e5_560a_5f27_9f8f_496b6781308e_TB5971_11 so that they average out to the value of the function at the point in question. Looking at the answer choices, only option D satisfies this requirement.

Question 6

If f and g are continuous functions with 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of If f and g are continuous functions...

Question 7

Find the numbers, if any, where the function  is discontinuous.

Accepted Answer

The answer of Find the numbers, if any, where the...

Question 8

Use continuity to evaluate the limit. 
A) 
B)0
C) 
D)1
E)

Accepted Answer

The answer of Use continuity to evaluate the limit. 
A)...

Question 9

Find the limit  .

Accepted Answer

The answer of Find the limit  ....

Question 10

For x = 5, determine whether f is continuous from the right, from the left, or neither.

Accepted Answer

The answer of For x = 5, determine whether f...

Question 11

Use the graph to determine where the function is discontinuous. 
A)At 0
B)On the interval 
C)At 
D)At 1

Accepted Answer

The answer of Use the graph to determine where the...

Question 12

Find a function g that agrees with f for  and is continuous on  .

Accepted Answer

The answer of Find a function g that agrees with...

Question 13

Let  Find the value of k that will make f continuous on 
A)3
B)28
C)-2
D)6

Accepted Answer

In order for f to be continuous, we need to ensure that the function is continuous at the point 11eaa3e5_560c_f75f_9f8f_cb235e2844cf_TB5971_00. To do so, we need to find the limit of f as it approaches this point from both directions:
lim(x->11eaa3e5_560c_f75f_9f8f_cb235e2844cf_TB5971_00+) f(x) = lim(x->11eaa3e5_560c_f75f_9f8f_cb235e2844cf_TB5971_00+) (5x + k)
= 5(11eaa3e5_560c_f75f_9f8f_cb235e2844cf_TB5971_00) + k
= 560e07d3_3a9c_7bdf_d2d1_cea0a6b92e49 + k

lim(x->11eaa3e5_560c_f75f_9f8f_cb235e2844cf_TB5971_00-) f(x) = lim(x->11eaa3e5_560c_f75f_9f8f_cb235e2844cf_TB5971_00-) (x^2 - 2)
= (11eaa3e5_560c_f75f_9f8f_cb235e2844cf_TB5971_00)^2 - 2
= 12cc7583_bf3e_b6e8_cf1f_c3e3f52acf3d

For f to be continuous at the given point, these two limits must be equal. Therefore, we have:

560e07d3_3a9c_7bdf_d2d1_cea0a6b92e49 + k = 12cc7583_bf3e_b6e8_cf1f_c3e3f52acf3d

Solving for k, we get:

k = 12cc7583_bf3e_b6e8_cf1f_c3e3f52acf3d - 560e07d3_3a9c_7bdf_d2d1_cea0a6b92e49
k = 2f2c
k = 3 (in decimal)

Therefore, the best choice is A) 3.

Question 14

Find the numbers, if any, where the function  is discontinuous.

Accepted Answer

The answer of Find the numbers, if any, where the...

Question 15

Find the interval(s) where  is continuous.
A) 
B) 
C) 
D)

Accepted Answer

The answer of Find the interval(s) where  is continuous.
A)...

Question 16

Find the limit  .

Accepted Answer

The answer of Find the limit  ....

Question 17

Use continuity to evaluate the limit.

Accepted Answer

The answer of Use continuity to evaluate the limit. ...

Question 18

Choose an equation from the following that expresses the fact that a function  is continuous at the number  .
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Choose an equation from the following that...

Question 19

If a rock is thrown upward on the planet Mars with a velocity of 10 m/s, its height in meters t seconds later is given by  . Find the average velocity over the time interval  .
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of If a rock is thrown upward on...

Question 20

Find the numbers, if any, where the function  is discontinuous.
A)5
B)-8
C) 
D)-2

Accepted Answer

The answer of Find the numbers, if any, where the...

Quiz 1: Functions and Limits

For what value of the constant c is the function f continuous on

Find the interval(s) where is continuous.

Determine where f is discontinuous.

Define the function at 0 so as to make it continuous at 0.

How would you define in order to make f continuous at ?

If f and g are continuous functions with

Find the numbers, if any, where the function is discontinuous.

Use continuity to evaluate the limit.

Find the limit .

For x = 5, determine whether f is continuous from the right, from the left, or neither.

Use the graph to determine where the function is discontinuous.

Find a function g that agrees with f for and is continuous on .

Let Find the value of k that will make f continuous on

Find the numbers, if any, where the function is discontinuous.

Find the interval(s) where is continuous.

Find the limit .

Use continuity to evaluate the limit.

Choose an equation from the following that expresses the fact that a function is continuous at the number .

If a rock is thrown upward on the planet Mars with a velocity of 10 m/s, its height in meters t seconds later is given by . Find the average velocity over the time interval .

Find the numbers, if any, where the function is discontinuous.