Understanding Limit Notation & Meaning

Question 1

Given a graph of a function f(x) that approaches y = 3 as x approaches 2 from both sides, what is lim(x→2) f(x)?

Accepted Answer

3

Answer

0

Answer

2

Answer

Cannot be determined from the graph

Question 2

A table shows values of g(x) as x approaches 0:


	
		
			x
			g(x)
		
		
			-0.1
			0.99
		
		
			-0.01
			0.9999
		
		
			-0.001
			0.999999
		
		
			0.001
			0.999999
		
		
			0.01
			0.9999
		
		
			0.1
			0.99
		
	


What is the best estimate for lim(x&rarr;0) g(x)?

Accepted Answer

1

Answer

0

Answer

0.99

Answer

Cannot be determined

Question 3

If lim(x→3-) f(x) = 5 and lim(x→3+) f(x) = 7, what can be said about lim(x→3) f(x)?

Accepted Answer

The limit does not exist

Answer

The limit is 5

Answer

The limit is 7

Answer

The limit is 6 (the average of 5 and 7)

Question 4

Which statement best describes the meaning of lim(x→c) f(x) = L?

Accepted Answer

As x gets arbitrarily close to c (but not equal to c), f(x) gets arbitrarily close to L

Answer

The value of f(x) at x = c is L

Answer

The function f(x) equals L for all x near c

Answer

The graph of f(x) passes through the point (c, L)

Question 5

Under which condition does a limit not exist?

Accepted Answer

When the function is unbounded as x approaches the point

Answer

When the function approaches the same value from both sides

Answer

When the function is defined at the point

Answer

When the function approaches a finite value as x approaches the point

Question 6

If a graph shows that as x approaches 1 from the left, f(x) approaches 4, and as x approaches 1 from the right, f(x) approaches 4, what can you conclude about lim(x→1) f(x)?

Accepted Answer

The limit is 4

Answer

The limit is 1

Answer

The limit does not exist

Answer

The limit is undefined

Question 7

What is the relationship between one-sided limits and the two-sided limit?

Accepted Answer

The two-sided limit exists if and only if both one-sided limits exist and are equal

Answer

The two-sided limit always exists if at least one one-sided limit exists

Answer

The two-sided limit is the average of the left and right limits

Answer

One-sided limits have no relationship to the two-sided limit

Question 8

Which of the following is NOT a way that a limit might fail to exist?

Accepted Answer

The function is undefined at the point

Answer

The function is unbounded as x approaches the point

Answer

The function oscillates infinitely as x approaches the point

Answer

The limit from the left does not equal the limit from the right

Question 9

If limx&rarr;0 sin(x)/x = 1, what does this tell us about the behavior of sin(x)/x near x = 0?

Accepted Answer

As x gets closer to 0, the value of sin(x)/x gets closer to 1

Answer

The function sin(x)/x equals 1 at x = 0

Answer

The function sin(x)/x is undefined at x = 0

Answer

As x gets larger, sin(x)/x approaches 1

Question 10

What does the notation limx&rarr;4 f(x) = 7 mean?

Accepted Answer

As x gets closer and closer to 4, f(x) gets closer and closer to 7

Answer

The function f(x) equals 7 when x equals 4

Answer

The function f(x) approaches 4 as x approaches 7

Answer

The value of f(4) is approximately 7

Question 11

What is the correct notation for "the limit of f(x) as x approaches 2 is 5"?

Accepted Answer

lim(x→2) f(x) = 5

Answer

f(2) = 5

Answer

lim(x→5) f(x) = 2

Answer

f(x) → 2 as x → 5

Question 12

If lim(x→0) f(x) = 1, which statement is true?

Accepted Answer

As x gets closer to 0, f(x) gets closer to 1

Answer

f(0) = 1

Answer

f(x) = 1 for all x near 0

Answer

The graph of f(x) has a hole at (0, 1)

Question 13

Given a table of values for f(x) where x approaches 2:

	
		
			x
			f(x)
		
		
			1.9
			4.9
		
		
			1.99
			4.99
		
		
			1.999
			4.999
		
		
			2.001
			5.001
		
		
			2.01
			5.01
		
		
			2.1
			5.1
		
	


What is the best estimate for lim(x&rarr;2) f(x)?

Accepted Answer

5

Answer

2

Answer

4.9

Answer

5.1

Question 14

Under which condition does a limit not exist?

Accepted Answer

When the left-hand limit equals the right-hand limit

Answer

When the function is defined at the point

Answer

When the function oscillates infinitely as x approaches the point

Answer

When the function approaches a finite value as x approaches the point

Question 15

Why might a graphical representation of a function miss important behavior near a point?

Accepted Answer

The scale of the graph might be too large to show rapid changes or oscillations

Answer

Graphs only show the general shape of functions

Answer

Graphs cannot represent vertical asymptotes

Answer

Graphs are always accurate representations of functions

Understanding Limit Notation & Meaning Live Quiz