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 \(\lim_{x\rightarrow 7}g(x)=6\)?
A 
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 \(\lim_{x\rightarrow 9}g(x)=5\) .