Question 1

Find the value of c guaranteed by the Intermediate Value Theorem. ​  ,  ,  ​

Accepted Answer

The answer of Find the value of c guaranteed by...

Question 2

Find the x-values (if any)at which the function  is not continuous.Which of the discontinuities are removable? ​

Accepted Answer

To identify the points of discontinuity, we need to check where the function is undefined or where the limit does not exist. Looking at the function, we notice that there is a variable in the denominator. For a fraction, the denominator cannot be zero. Therefore, the function is undefined at any value of x that makes the denominator zero.

Setting the denominator equal to zero, we get:
(x-3)(x+2)(x-1) = 0 
which has roots at x=3, x=-2, and x=1.

Therefore, the function is not continuous at x=3, x=-2, and x=1.

To determine if any of these discontinuities are removable, we need to check if the limits exist at these points. Evaluating the limits of the function as x approaches each of these points, we find:

lim(x-->3) 11eac44f_ede8_0de9_bedf_a1418ccc8776_TB7497_11 = 5/18
lim(x-->-2) 11eac44f_ede8_0dea_bedf_5fd85dbf31df_TB7497_11 = DNE
lim(x-->1) 11eac44f_ede8_0deb_bedf_6275d6d93e66_TB7497_11 = -5/2

The limit at x=3 exists and is finite, so the discontinuity at x=3 is removable. The limit at x=1 exists but is not equal to the function value, so the discontinuity at x=1 is also removable. However, the limit at x=-2 does not exist or is infinite, so the discontinuity at x=-2 is not removable.

Therefore, the function has removable discontinuities at x=3 and x=1, and a non-removable discontinuity at x=-2, giving us choice C as the correct answer.

Question 3

Find the value of c guaranteed by the Intermediate Value Theorem. ​  ,  ,  ​

Accepted Answer

The answer of Find the value of c guaranteed by...

Question 4

Find the limit. ​  ​

Accepted Answer

The answer of Find the limit. ​  ​
...

Question 5

Find the constant a such that the function ​  ​
Is continuous on the entire real line.
​

Accepted Answer

The answer of Find the constant a such that the...

Question 6

A long distance phone service charges $0.45 for the first 11 minutes and $0.1 for each additional minute or fraction thereof.Use the greatest integer function to write the cost C of a call in terms of time t (in minutes). ​

Accepted Answer

The answer of A long distance phone service charges $0.45...

Question 7

Discuss the continuity of the function  . ​  ​

Accepted Answer

The answer of Discuss the continuity of the function ...

Question 8

Find the x-values (if any)at which  is not continuous. ​

Accepted Answer

The answer of Find the x-values (if any)at which ...

Question 9

Find the x-values (if any)at which the function  is not continuous.Which of the discontinuities are removable? ​

Accepted Answer

The answer of Find the x-values (if any)at which the...

Question 10

Find all values of c such that f is continuous on  . ​  ​

Accepted Answer

The answer of Find all values of c such that...

Question 11

Find the x-values (if any)at which  is not continuous. ​

Accepted Answer

The answer of Find the x-values (if any)at which ...

Question 12

Find the x-values (if any)at which the function  is not continuous.Which of the discontinuities are removable? ​

Accepted Answer

The answer of Find the x-values (if any)at which the...

Question 13

Find the limit. ​  ​

Accepted Answer

The answer of Find the limit. ​  ​
...

Question 14

Find the limit. ​  ​

Accepted Answer

The answer of Find the limit. ​  ​
...

Question 15

Find the limit. ​  ​

Accepted Answer

The answer of Find the limit. ​  ​
...

Question 16

Find the lmit. ​  ​

Accepted Answer

The answer of Find the lmit. ​  ​
...

Question 17

Find the limit. ​  ​

Accepted Answer

The answer of Find the limit. ​  ​
...

Question 18

Find the constant  such that the function ​  ​
Is continuous on the entire real line.
​

Accepted Answer

For a polynomial function to be continuous on the entire real line, it is necessary that the degree of the polynomial function is at least 1 and that the coefficient of the term with the highest degree is nonzero.

The given function 11eac44f_ede9_467a_bedf_ad025c4b9124_TB7497_00 has a degree of 4.

To ensure continuity, we need the coefficient of the term with the highest degree (which is the term with x^4) to be nonzero. The coefficient of this term is 11eac44f_ede9_1f69_bedf_ed220d0be562_TB7497_00.

Therefore, the answer is E) 15, since 15 is the only nonzero option provided.

Question 19

Find the limit. ​  ​

Accepted Answer

The answer of Find the limit. ​  ​
...

Question 20

Find the limit (if it exists).Note that  represents the greatest integer function. ​  ​

Accepted Answer

The answer of Find the limit (if it exists).Note that...

Quiz 2: Limits and Their Properties

Find the value of c guaranteed by the Intermediate Value Theorem. , ,

Find the x-values (if any) at which the function is not continuous.Which of the discontinuities are removable?

Find the value of c guaranteed by the Intermediate Value Theorem. , ,

Find the limit.

Find the constant a such that the function Is continuous on the entire real line.

A long distance phone service charges $0.45 for the first 11 minutes and $0.1 for each additional minute or fraction thereof.Use the greatest integer function to write the cost C of a call in terms of time t (in minutes) .

Discuss the continuity of the function .

Find the x-values (if any) at which is not continuous.

Find the x-values (if any) at which the function is not continuous.Which of the discontinuities are removable?

Find all values of c such that f is continuous on .

Find the x-values (if any) at which is not continuous.

Find the x-values (if any) at which the function is not continuous.Which of the discontinuities are removable?

Find the limit.

Find the limit.

Find the limit.

Find the lmit.

Find the limit.

Find the constant such that the function Is continuous on the entire real line.

Find the limit.

Find the limit (if it exists) .Note that represents the greatest integer function.

Quiz 2: Limits and Their Properties

Find the value of c guaranteed by the Intermediate Value Theorem. ​ , , ​

Find the x-values (if any) at which the function is not continuous.Which of the discontinuities are removable? ​

Find the value of c guaranteed by the Intermediate Value Theorem. ​ , , ​

Find the limit. ​ ​

Find the constant a such that the function ​ ​ Is continuous on the entire real line. ​

A long distance phone service charges $0.45 for the first 11 minutes and $0.1 for each additional minute or fraction thereof.Use the greatest integer function to write the cost C of a call in terms of time t (in minutes) . ​

Discuss the continuity of the function . ​ ​

Find the x-values (if any) at which is not continuous. ​

Find the x-values (if any) at which the function is not continuous.Which of the discontinuities are removable? ​

Find all values of c such that f is continuous on . ​ ​

Find the x-values (if any) at which is not continuous. ​

Find the x-values (if any) at which the function is not continuous.Which of the discontinuities are removable? ​

Find the limit. ​ ​

Find the limit. ​ ​

Find the limit. ​ ​

Find the lmit. ​ ​

Find the limit. ​ ​

Find the constant such that the function ​ ​ Is continuous on the entire real line. ​

Find the limit. ​ ​

Find the limit (if it exists) .Note that represents the greatest integer function. ​ ​

Find the value of c guaranteed by the Intermediate Value Theorem. , ,

Find the x-values (if any) at which the function is not continuous.Which of the discontinuities are removable?

Find the value of c guaranteed by the Intermediate Value Theorem. , ,

Find the limit.

Find the constant a such that the function Is continuous on the entire real line.

A long distance phone service charges $0.45 for the first 11 minutes and $0.1 for each additional minute or fraction thereof.Use the greatest integer function to write the cost C of a call in terms of time t (in minutes) .

Discuss the continuity of the function .

Find the x-values (if any) at which is not continuous.

Find the x-values (if any) at which the function is not continuous.Which of the discontinuities are removable?

Find all values of c such that f is continuous on .

Find the x-values (if any) at which is not continuous.

Find the x-values (if any) at which the function is not continuous.Which of the discontinuities are removable?

Find the limit.

Find the limit.

Find the limit.

Find the lmit.

Find the limit.

Find the constant such that the function Is continuous on the entire real line.

Find the limit.

Find the limit (if it exists) .Note that represents the greatest integer function.