Quiz about Special Trig Limits and Continuity

Question 1

Which is TRUE?

Accepted Answer

$$\lim_{x\rightarrow0}\ \frac{\sin x}{2x}=0.5$$

Answer

$$\lim_{x\rightarrow\pi}\ \frac{\sin x}{x}=1$$

Answer

$$\lim_{x\rightarrow1}\ \frac{x}{\sin x}\ =\ 1\ $$

Answer

$$\lim_{x\rightarrow1}\ \frac{1-\cos x}{x}$$

Question 2

Which is/are the conditions for a function to be continuous at x = a?

Accepted Answer

all of the choices

Answer

$$f\left(a\right)\ $$ is defined

Answer

$$\lim_{x\rightarrow a}\ f\left(x\right)\ exists$$

Answer

$$\lim_{x\rightarrow a}\ f\left(x\right)\ =\ f\left(a\right)$$

Question 3

Which is TRUE about the given graph?

Accepted Answer

The function has a removable discontinuity at x = -2.

Answer

The function has infinite discontinuity at x = -2.

Answer

The function has a jump discontinuity at x = -2.

Answer

The function has a removable discontinuity at x = 3.

Question 4

Which is TRUE about the given graph?

Accepted Answer

It has an infinite discontinuity at x = -4.

Answer

It has an infinite discontinuity at x = 4.

Answer

It has a jump discontinuity at x = -4.

Answer

It has a removable discontinuity at x = -4.

Question 5

If at x = 1, the left hand limit of f(x) is 2, and its right hand limit is 0, then f(x) has _____.

Accepted Answer

a jump discontinuity at x = 1

Answer

an infinite discontinuity at x = 1

Answer

a removable discontinuity at x = 1

Question 6

Which type of discontinuity has a limit that exists at x = a?

Accepted Answer

removable

Answer

infinite

Answer

jump

Question 7

If $$\lim_{x\rightarrow-6^+}\ f\left(x\right)\ =\ +\infty$$ , then f(x) has _____

Accepted Answer

an infinite discontinuity at x = -6.

Answer

a removable discontinuity at x = -6

Answer

a jump discontinuity at x = -6

Question 8

What is f(-4)?

Accepted Answer

undefined

Answer

-4

Answer

-1

Answer

indeterminate

Question 9

Which is FALSE?

Accepted Answer

f(x) is continuous at x = -4

Answer

$$\lim_{x\rightarrow-4}\ f\left(x\right)\ exists$$

Answer

$$\lim_{x ightarrow-4}\ f\left(x ight)\ e\ f\left(-4 ight)$$

Answer

f(x) is discontinuous at x = -4

Question 10

Check all true statements.

Accepted Answer

f(0) is defined

Accepted Answer

$$\lim_{x\rightarrow0}\ f\left(x\right)\ exists$$

Accepted Answer

$$\lim_{x\rightarrow0}\ f\left(x\right)\ =\ f\left(0\right)$$

Accepted Answer

f(x) is continuous at x = 0

Question 11

If $$f\left(x\right)\ =\ \frac{x+4}{x+5}$$ , then _____.

Accepted Answer

f(x) has an infinite discontinuity at x = -5

Answer

f(x) has an infinite discontinuity at x = -4

Answer

f(x) is discontinuous at x = -4

Answer

f(x) is continuous at x = -5

Question 12

Refer to the graph of f(x):

f(x) has removable discontinuities at _____.

Accepted Answer

x = 2

Accepted Answer

x = 3

Answer

x = -1

Answer

x = 7

Question 13

Refer to the given graph:

f(x) has infinite discontinuities at _____.

Accepted Answer

x = -1

Accepted Answer

x = 5

Answer

x = 2

Answer

x = 7

Special Trig Limits and Continuity

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