Question 1

What type of discontinuity does a function

f(x)

have if

\lim_{{x 	o c}} f(x)

exists but

f(c)

is undefined?

Accepted Answer

Removable discontinuity

Answer

Infinite discontinuity

Answer

Jump discontinuity

Answer

Continuous function

Question 2

Which of the following is true about a continuous function at a point

f(x)

?

Accepted Answer

The limit of the function as

f(x)

approaches

\lim_{{x 	o c}} f(x)

is equal to the function's value at

f(c)

.

Answer

The derivative of the function does not exist at

f(x)

.

Answer

The function is undefined at

f(x)

.

Answer

The function has a non-removable discontinuity at

f(x)

.

Question 3

Which type of discontinuity occurs when a function has a jump at a certain point on its graph?

Accepted Answer

Jump discontinuity

Answer

Continuous function

Answer

Removable discontinuity

Answer

Infinite discontinuity

Question 4

If a function is differentiable at a point

f(x)

, what can be said about its continuity at that point?

Accepted Answer

The function is continuous at

f(x)

.

Answer

The derivative does not exist at

f(x)

.

Answer

The function is not continuous at

f(x)

.

Answer

The function has a jump discontinuity at

f(x)

.

Question 5

What type of discontinuity is present if the limit of a function approaches infinity as

f(x)

approaches

\lim_{{x 	o c}} f(x)

?

Accepted Answer

Infinite discontinuity

Answer

Removable discontinuity

Answer

Continuous function

Answer

Jump discontinuity

Question 6

Which of the following statements is true about a function that has a removable discontinuity at

f(x)

?

Accepted Answer

The limit as

f(x)

approaches

\lim_{{x 	o c}} f(x)

exists.

Answer

The function is not defined for any value of

f(x)

near

\lim_{{x 	o c}} f(x)

.

Answer

The function tends to infinity as

f(x)

approaches

\lim_{{x 	o c}} f(x)

.

Answer

The left-hand and right-hand limits are different.

Question 7

Which condition must be true for a function

f(x)

to be continuous at

\lim_{{x 	o c}} f(x)

?

Accepted Answer

\lim_{{x 	o c}} f(x) = f(c)

Answer

The limit

f(x)

does not exist

Answer

\lim_{{x 	o c}} f(x) = f(c)

has a jump at

c

Answer

\lim_{{x 	o c}} f(x) = f(c)

is undefined

Question 8

What is the primary difference between a jump discontinuity and a removable discontinuity?

Accepted Answer

In a jump discontinuity, the left-hand and right-hand limits exist but are not equal, while in a removable discontinuity, they are equal.

Answer

In a removable discontinuity, the limits do not exist; in a jump discontinuity, they do.

Answer

A removable discontinuity involves an infinite limit; a jump discontinuity does not.

Answer

A jump discontinuity means the function is undefined for all

f(x)

; a removable discontinuity does not.

Question 9

What is the derivative of f(x) = 3x^3 - 5x + 2?

Accepted Answer

\lim_{{x 	o c}} f(x) = f(c)

Answer

\lim_{{x 	o c}} f(x) = f(c)

Answer

\lim_{{x 	o c}} f(x) = f(c)

Answer

\lim_{{x 	o c}} f(x) = f(c)

Question 10

Consider the function f(x) = x^3 - 6x^2 + 9x + 15. What is the local minimum point?

Accepted Answer

x = 2

Answer

x = 0

Answer

x = 3

Answer

x = 1

Question 11

Which trigonometric function is equal to the ratio of the adjacent side to the hypotenuse in a right triangle?

Accepted Answer

cosine

Answer

sine

Answer

tangent

Answer

cotangent

Question 12

Which trigonometric function has a range of [-1, 1]?

Accepted Answer

sine

Answer

tangent

Answer

secant

Answer

cotangent

Question 13

Which of the following is the correct expression for the Pythagorean identity?

Accepted Answer

\lim_{{x 	o c}} f(x) = f(c)

Answer

\lim_{{x 	o c}} f(x) = f(c)

Answer

\lim_{{x 	o c}} f(x) = f(c)

Answer

\lim_{{x 	o c}} f(x) = f(c)

Question 14

What is the identity for tangent in terms of sine and cosine?

Accepted Answer

\lim_{{x 	o c}} f(x) = f(c)

Answer

\lim_{{x 	o c}} f(x) = f(c)

Answer

\lim_{{x 	o c}} f(x) = f(c)

Answer

\lim_{{x 	o c}} f(x) = f(c)

Question 15

Which trigonometric identity represents the reciprocal of sine?

Accepted Answer

\lim_{{x 	o c}} f(x) = f(c)

Answer

\lim_{{x 	o c}} f(x) = f(c)

Answer

\lim_{{x 	o c}} f(x) = f(c)

Answer

\lim_{{x 	o c}} f(x) = f(c)

Question 16

What is the trigonometric identity for

f(x)

?

Accepted Answer

\lim_{{x 	o c}} f(x) = f(c)

Answer

\lim_{{x 	o c}} f(x) = f(c)

Answer

\lim_{{x 	o c}} f(x) = f(c)

Answer

\lim_{{x 	o c}} f(x) = f(c)

Question 17

What is the identity for the cotangent of an angle in terms of cosine and sine?

Accepted Answer

\lim_{{x 	o c}} f(x) = f(c)

Answer

\lim_{{x 	o c}} f(x) = f(c)

Answer

\lim_{{x 	o c}} f(x) = f(c)

Answer

\lim_{{x 	o c}} f(x) = f(c)

Question 18

Which trigonometric identity expresses the secant in terms of cosine?

Accepted Answer

\lim_{{x 	o c}} f(x) = f(c)

Answer

\lim_{{x 	o c}} f(x) = f(c)

Answer

\lim_{{x 	o c}} f(x) = f(c)

Answer

\lim_{{x 	o c}} f(x) = f(c)

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