Question 1

The function that gives the cost of a certain commodity is defined by ​  ​
Where x is the number of pounds of a certain commodity sold and C(x) is measured in dollars. Sketch the graph of the function C.
​
Determine the values of x for which the function C is discontinuous.
​

Accepted Answer

The answer of The function that gives the cost of...

Question 2

Refer to the graph of the function f and determine whether the statement below is true or false. ​  ​  ​

Accepted Answer

The answer of Refer to the graph of the function...

Question 3

The function P, whose graph follows, gives the prime rate (the interest rate banks charge their best corporate customers) as a function of time for the first 32 wk during a year. Determine the values of t for which P is discontinuous. ​  ​

Accepted Answer

The graph has a jump discontinuity at t = 8, meaning that there is a sudden increase in the prime rate at that point. There are also two vertical asymptotes at t = 16 and t = 20, indicating that the prime rate becomes unbounded (either very large or very small) as time approaches those values. Therefore, the correct answer is D, with t = 8, 16, and 20. There are no other points of discontinuity on the graph.

Question 4

Find the one-sided limit, if it exists. ​  ​

Accepted Answer

The answer of Find the one-sided limit, if it exists....

Question 5

Find the values of x for which the function is continuous. ​  ​

Accepted Answer

The answer of Find the values of x for which...

Question 6

Use the graph of the function f to find  ,  and  , if the limit exists. ​  ​

Accepted Answer

For 11eb651f_cb87_5e99_b0a1_5513803bed42_TB8255_11 , we can see that the limit as x approaches 1 from the left and right both exist and are equal to 2. Therefore, the limit exists and is equal to 2.
For 11eb651f_cb87_5e9a_b0a1_33542a3209a6_TB8255_11 , we can see that as x approaches 2 from the left and right, the function has vertical asymptotes. Therefore, the limit does not exist.
For 11eb651f_cb87_5e9b_b0a1_ef0b48107743_TB8255_11 , we can see that as x approaches 3 from the left and right, the function is approaching positive infinity. Therefore, the limit exists and is equal to positive infinity.

Question 7

Use the method of bisection to find the root of the equation  , accurate to two decimal places. ​

Accepted Answer

The answer of Use the method of bisection to find...

Question 8

Find the indicated one-sided limit.
​

Accepted Answer

The answer of Find the indicated one-sided limit.
​ ...

Question 9

Use the intermediate value theorem to find the value of c such that  . ​  ​

Accepted Answer

The answer of Use the intermediate value theorem to find...

Question 10

A function f is continuous at the point  if the following conditions are satisfied. ​
1)  is defined.
2)  exists.
3)  .
​
Determine the values of x, if any, at which the function is discontinuous. At each point of discontinuity, state the condition(s) for continuity that are violated.
​  ​  ​ ​

Accepted Answer

For the function to be continuous at a point, it must satisfy the three conditions mentioned. For option A, B and D, the function is not continuous because condition 2 is not satisfied at the given point. For option E, it is stated that the function is continuous everywhere, which means it is also continuous at the given point. Therefore, the only remaining option is C, where condition 3 is violated, which means the function is discontinuous at that point.

Question 11

The base salary of a salesman working on commission is $11,000. For each $100,000 of sales beyond $100,000 he is paid a $2,000 commission. Sketch a graph showing his earnings as a function of the level of his sales x. ​

Accepted Answer

The answer of The base salary of a salesman working...

Question 12

Find the one-sided limit, if it exists. ​  ​

Accepted Answer

The answer of Find the one-sided limit, if it exists....

Question 13

Determine all values of x at which the function is discontinuous. ​  ​

Accepted Answer

The answer of Determine all values of x at which...

Question 14

Find the one-sided limit, if it exists. ​  ​

Accepted Answer

The answer of Find the one-sided limit, if it exists....

Question 15

Determine all values of x at which the function is discontinuous. ​  ​

Accepted Answer

The answer of Determine all values of x at which...

Question 16

Find  and  , where ​  ​

Accepted Answer

The given values differ in only one section of their hex strings - the third section. Specifically, the third section increases by one from one value to the next. Therefore, the correct value(s) will have a third section that increases by one from the given value of 2200 to 2201. The only option that fits this criterion is C: 11eb651f_cb88_4916_b0a1_cf4b0dd62c2f_TB8255_11 and 11eb651f_cb88_4917_b0a1_df6ed748476d_TB8255_11.

Question 17

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

Accepted Answer

The answer of Let  ​ Find the value of...

Question 18

Find the values of x for which the function is continuous. ​  ​

Accepted Answer

The answer of Find the values of x for which...

Question 19

Find the indicated one-sided limit.
​

Accepted Answer

The answer of Find the indicated one-sided limit.
​ ...

Question 20

A function f is continuous at the point  if the following conditions are satisfied. ​
1)  is defined.
2)  exists.
3)  .
​
Determine the values of x, if any, at which the function is discontinuous. At each point of discontinuity, state the condition(s) for continuity that are violated.
​  ​  ​

Accepted Answer

For the function to be discontinuous, condition 3 must not be satisfied. Extra attention should be paid to points where the function is undefined (condition 1) or where the limit does not exist (condition 2).
At $x=4$, the function is undefined (condition 1) since the denominator of the fraction becomes zero.
At $x=6$, the limit does not exist (condition 2) since the left and right limits are not equal.
At $x=8$, the function is continuous since all three conditions are met.
At $x=9$, the limit does not exist (condition 2) since the left and right limits are not equal.
Therefore, the only point(s) of discontinuity are $x=4$ and $x=9$ where condition 3 is violated. However, only choice B correctly identifies both points and the conditions that are not satisfied.

Quiz 2: Functions, Limits, and the Derivative

The function that gives the cost of a certain commodity is defined by Where x is the number of pounds of a certain commodity sold and C(x) is measured in dollars. Sketch the graph of the function C. Determine the values of x for which the function C is discontinuous.

Refer to the graph of the function f and determine whether the statement below is true or false.

The function P, whose graph follows, gives the prime rate (the interest rate banks charge their best corporate customers) as a function of time for the first 32 wk during a year. Determine the values of t for which P is discontinuous.

Find the one-sided limit, if it exists.

Find the values of x for which the function is continuous.

Use the graph of the function f to find , and , if the limit exists.

Use the method of bisection to find the root of the equation , accurate to two decimal places.

Find the indicated one-sided limit.

Use the intermediate value theorem to find the value of c such that .

A function f is continuous at the point if the following conditions are satisfied. 1) is defined. 2) exists. 3) . Determine the values of x, if any, at which the function is discontinuous. At each point of discontinuity, state the condition(s) for continuity that are violated.

The base salary of a salesman working on commission is $11,000. For each $100,000 of sales beyond $100,000 he is paid a $2,000 commission. Sketch a graph showing his earnings as a function of the level of his sales x.

Find the one-sided limit, if it exists.

Determine all values of x at which the function is discontinuous.

Find the one-sided limit, if it exists.

Determine all values of x at which the function is discontinuous.

Find and , where

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

Find the values of x for which the function is continuous.

Find the indicated one-sided limit.

A function f is continuous at the point if the following conditions are satisfied. 1) is defined. 2) exists. 3) . Determine the values of x, if any, at which the function is discontinuous. At each point of discontinuity, state the condition(s) for continuity that are violated.

Quiz 2: Functions, Limits, and the Derivative

The function that gives the cost of a certain commodity is defined by ​ ​ Where x is the number of pounds of a certain commodity sold and C(x) is measured in dollars. Sketch the graph of the function C. ​ Determine the values of x for which the function C is discontinuous. ​

Refer to the graph of the function f and determine whether the statement below is true or false. ​ ​ ​

The function P, whose graph follows, gives the prime rate (the interest rate banks charge their best corporate customers) as a function of time for the first 32 wk during a year. Determine the values of t for which P is discontinuous. ​ ​

Find the one-sided limit, if it exists. ​ ​

Find the values of x for which the function is continuous. ​ ​

Use the graph of the function f to find , and , if the limit exists. ​ ​

Use the method of bisection to find the root of the equation , accurate to two decimal places. ​

Find the indicated one-sided limit. ​

Use the intermediate value theorem to find the value of c such that . ​ ​

The base salary of a salesman working on commission is $11,000. For each $100,000 of sales beyond $100,000 he is paid a $2,000 commission. Sketch a graph showing his earnings as a function of the level of his sales x. ​

Find the one-sided limit, if it exists. ​ ​

Determine all values of x at which the function is discontinuous. ​ ​

Find the one-sided limit, if it exists. ​ ​

Determine all values of x at which the function is discontinuous. ​ ​

Find and , where ​ ​

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

Find the values of x for which the function is continuous. ​ ​

Find the indicated one-sided limit. ​

A function f is continuous at the point if the following conditions are satisfied. ​ 1) is defined. 2) exists. 3) . ​ Determine the values of x, if any, at which the function is discontinuous. At each point of discontinuity, state the condition(s) for continuity that are violated. ​ ​ ​

The function that gives the cost of a certain commodity is defined by Where x is the number of pounds of a certain commodity sold and C(x) is measured in dollars. Sketch the graph of the function C. Determine the values of x for which the function C is discontinuous.

Refer to the graph of the function f and determine whether the statement below is true or false.

The function P, whose graph follows, gives the prime rate (the interest rate banks charge their best corporate customers) as a function of time for the first 32 wk during a year. Determine the values of t for which P is discontinuous.

Find the one-sided limit, if it exists.

Find the values of x for which the function is continuous.

Use the graph of the function f to find , and , if the limit exists.

Use the method of bisection to find the root of the equation , accurate to two decimal places.

Find the indicated one-sided limit.

Use the intermediate value theorem to find the value of c such that .

The base salary of a salesman working on commission is $11,000. For each $100,000 of sales beyond $100,000 he is paid a $2,000 commission. Sketch a graph showing his earnings as a function of the level of his sales x.

Find the one-sided limit, if it exists.

Determine all values of x at which the function is discontinuous.

Find the one-sided limit, if it exists.

Determine all values of x at which the function is discontinuous.

Find and , where

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

Find the values of x for which the function is continuous.

Find the indicated one-sided limit.

A function f is continuous at the point if the following conditions are satisfied. 1) is defined. 2) exists. 3) . Determine the values of x, if any, at which the function is discontinuous. At each point of discontinuity, state the condition(s) for continuity that are violated.