Question
If \(\lim_{x\rightarrow 6}f(x)\) exists with \(\lim_{x\rightarrow 6}f(x)< 8\) and f(6)=12 , which of the following statements must be false?
A \(\lim_{x\rightarrow 6^{-}}f(x)=0\)
B \(\lim_{x\rightarrow 6^{+}}f(x)< 8\)
C \(\lim_{x\rightarrow 6^{-}}f(x)=\lim_{x\rightarrow 6^{+}}f(x)\)
D f is continuous at x=6.
Answer/Explanation
Ans:D
Since \(\lim_{x\rightarrow 6}f(x)< 8\) and f(6)=12. It is false that \( \lim_{x\rightarrow 6}f(x)=6f(x)\) .Therefore,
cannot be continuous at
.
Question
Let f be the function defined above. Which of the following statements is true?
A f is continuous at x=1.
B f is not continuous at x=1 because f(1) does not exist.
C f is not continuous at x=1 because \(\lim_{x\rightarrow 1^{-}}f(x)\neq \lim_{x\rightarrow 1^{+}}f(x)\).
D f is not continuous at x=1 because \(\lim_{x\rightarrow 1}f(x)\) does not exist.
Answer/Explanation
Ans:B
Question
Which of the following functions is continuous at
?
A 
B 
C 
D 
Answer/Explanation
Ans:C
Question
For what value of h is 
continuous at \(x=\frac{5}{2}\) ?
(A) 0
(B) 3
(C) \(x=\frac{25}{2}\)
(D) \(x=\frac{19}{2}\)
Answer/Explanation
Ans:(D)
Since \(\lim_{x\rightarrow \frac{5}{2}}\frac{6x^{2}-11x-10}{2x-5}=\lim_{x\rightarrow \frac{5}{2}}\frac{(2x-5)(3x+2)}{2x-5}=\lim_{x\rightarrow \frac{5}{2}}3x+2=\frac{19}{2}\)