Limits and Early Continuity (AP use after 1.12)

The graph of the function f is shown. Which of the following statements is FALSE?

• $\lim_{x\rightarrow2}f\left(x\right)$ exists

• $\lim_{x\rightarrow3}f\left(x\right)$ exists

• $\lim_{x\rightarrow4}f\left(x\right)$ exists

• $\lim_{x\rightarrow5}f\left(x\right)$ exists

• The function f is continuous at x=3

Tags

CCSS.8.F.A.1

CCSS.HSF.IF.B.5

The graph of the function f is shown. At what value of x does f have a jump discontinuity?

• 1

• 3

• 7

• 10

Tags

CCSS.HSF-IF.C.7D

The graph of a function f is shown in the figure above. Which of the following statements is true?

• $f\left(a\right)=2$

• f is continuous at x=a

• $\lim_{x\rightarrow a}f\left(x\right)=1$

• $\lim_{x\rightarrow a}f\left(x\right)=2$

• $\lim_{x\rightarrow a}f\left(x\right)$ does not exist

 $\lim_{x\rightarrow0}\frac{2x^6+6x^3}{4x^5+3x^3}$  is

• 0

• 1/2

• 1

• 2

• DNE

 $\lim_{x\rightarrow-3}\frac{x^2-9}{x^2-2x-15}$  is

• 0

• 3/5

• 3/4

• 1

• DNE

 $\lim_{x\rightarrow2}\frac{x^2+x-6}{x^2-4}$  is

• -1/4

• 0

• 1

• 5/4

• DNE

 $\lim_{x\rightarrow0}\frac{5x^4+8x^2}{3x^4-16x^2}$  is

• -1/2

• 0

• 1

• 5/3

• DNE

Let f be the function given by

 $f\left(x\right)=\frac{\left(x-2\right)^2\left(x+3\right)}{\left(x-2\right)\left(x+1\right)}$  .  For which of the following values of x is f not continuous?

• -3 and -1

• -3, -1, and 2

• -1

• -1 and 2

• 2

Tags

CCSS.HSF-IF.C.7D

If f is a continuous function such that f(2)=6, which of the following statements must be true?

• $\lim_{x\rightarrow1}f\left(2x\right)=3$

• $\lim_{x\rightarrow2}f\left(2x\right)=6$

• $\lim_{x\rightarrow2}\frac{f\left(x\right)-f\left(2\right)}{x-2}=6$

• $\lim_{x\rightarrow2}f\left(x^2\right)=36$

• $\lim_{x\rightarrow2}\left[f\left(x\right)\right]^2=36$

The graph of a function f is shown Which of the following limits does not exist?

• $\lim_{x\rightarrow1^-}f\left(x\right)$

• $\lim_{x\rightarrow1}f\left(x\right)$

• $\lim_{x\rightarrow3^-}f\left(x\right)$

• $\lim_{x\rightarrow3}f\left(x\right)$

• $\lim_{x\rightarrow5}f\left(x\right)$

Tags

CCSS.HSF-IF.C.7B