AP Calculus AB: 1.2 Defining Limits and Using Limit Notation – Exam Style questions with Answer- MCQ

Question

The graph of the function f is shown above. What is  \(\lim_{x\rightarrow 2}f(x)\)

A.  \(\frac{1}{2}\)

B. 1

C. 4

D. The limit does not exist.

▶️Answer/Explanation

Ans: C

As x approaches 2, the function values approach 4. The fact that f(2)=1 has no bearing on the value of the limit.

Question

The graph of the function f is shown above. What is  \(\lim_{x\rightarrow 2}f(x)\)

A. 0

B. 1

C. 2

D. The limit does not exist.

▶️Answer/Explanation

Ans : C

As x approaches 2, the function values approach 2. The fact that f(2)=1 has no bearing on the value of the limit.

Question

On the following tables ,which best reflects the values of a function g for which \(\lim_{x\rightarrow 7}g(x)=6\)?

B

C

D

▶️Answer/Explanation

Ans :B

The values of g(x) in this table are increasing toward 6 as x approaches 7 from left ,and they are also increasing toward 6 as x approaches 7 from the right.The table therefore suggests that \(\lim_{x\rightarrow 7^{-}}g(x)=6=\lim_{x\rightarrow 7^{+}g(x)}\) and hence that \(\lim_{x\rightarrow 7}g(x)=6\).

Question

Of the following tables, which best reflects the values of a function gg for which \(\lim_{x\rightarrow 9}g(x)=5\) ?

▶️Answer/Explanation

Ans:B
Correct. The values of g(x)g(x) in this table are increasing toward 5 as xx approaches 9 from the left, and they are also increasing toward 5 as xx approaches 9 from the right. The table therefore suggests that \(\lim_{x\rightarrow 9^{-}}g(x)=5=\lim_{x\rightarrow 9^{+}}g(x)\) and hence that \(\lim_{x\rightarrow 9}g(x)=5\) .

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