AP Calculus AB: 1.11 Defining Continuity at a Point - Exam Style questions with Answer- MCQ

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Question

For any function f, which of the following statements must be true?

I If f is defined at x = a, then $\lim_{x\rightarrow a}f(x)=f(a)$ .

II If f is continuous at x = a, then $\lim_{x\rightarrow a}f(x)=f(a)$ .

III If f is differentiable at x = a, then $\lim_{x\rightarrow a}f(x)=f(a)$ .

A III only

B I and II only

C II and III only

D I, II, and III

▶️Answer/Explanation

Ans:C

Question

If the function f is continuous for all real numbers and if $f(x)=\frac{{x^{2}-4}}{x+2}$ when $x\neq 2$ ,then f(-2)=

A -4

B -2

C -1

D 0

E 2

▶️Answer/Explanation

Ans:A

Question

Let f be the function defined by $f (x) = {\begin{matrix} \begin{array}{l} x^{2} + 2 \\ 6 x + k \end{array} & \begin{array}{l} for x \leq 3, \\ for x > 3. \end{array} \end{matrix}$ If f is continuous at x=3,what is the value of k?

A -7

B 2

C 3

D 7

E There is no such value of k

▶️Answer/Explanation

.Ans:A

Question

Let $f$ be the piecewise function defined above. Which of the following statements is false?

A $f$ is continuous at $x equals 1$ .

B $f$ is continuous at $x equals 2$ .

C $f$ is continuous at $x equals 3$ .

D $f$ is continuous at $x equals 4$

▶️Answer/Explanation

Ans:C

The statement is false because $\lim_{x\rightarrow 3}f(x)=-3$ but f(3)=4 .In order for $f$ to be continuous at $x equals 3$

AP Calculus AB: 1.11 Defining Continuity at a Point – Exam Style questions with Answer- MCQ

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