2.2 - Calculus - Continuity and Limits

At x=a there is a _________ discontinuity.

Tags

CCSS.HSA.APR.B.2

CCSS.HSA.APR.B.3

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7

CCSS.HSA.REI.D.10

Which of the following best describes the continuity at x = 2?

• Jump Discontinuity

• Removable Discontinuity

• Continuous

• Infinite Discontinuity

Which of the following best describes the continuity at x = 1?

• Continuous

• Removable Discontinuity

• Infinite Discontinuity

• Jump Discontinuity

Tags

CCSS.HSF.IF.C.7

CCSS.HSF.IF.B.4

At which x-value is there a jump discontinuity?

• $x=-3$

• $x=-6$

• $x=1$

• $x=2$

Tags

CCSS.HSF-IF.C.7B

Which of the following best describes the continuity at x = -4?

• Continuous

• Removable Discontinuity

• Infinite Discontinuity

• Jump Discontinuity

Tags

CCSS.HSF-IF.C.7D

Is f(x) continuous at x = a, and why?

• No, $\lim_{x\rightarrow a^-}f\left(x\right)\ne\lim_{x\rightarrow a^+}f\left(x\right)$

• No, $\lim_{x\rightarrow a}f\left(x\right)\ne f\left(a\right)$

• Yes, $\lim_{x\rightarrow a^-}f\left(x\right)=\lim_{x\rightarrow a^+}f\left(x\right)$

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

Tags

CCSS.HSF.IF.C.7

CCSS.HSF.IF.B.4

At x = 1 there is a _______ discontinuity.

Tags

CCSS.HSF-IF.C.7B

Is the function continuous at x = 2, and why?

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

• Yes, $\lim_{x\rightarrow2^-}f\left(x\right)=\lim_{x\rightarrow2^+}f\left(x\right)$

• No, $\lim_{x\rightarrow2^-}f\left(x\right)\ne\lim_{x\rightarrow2^+}f\left(x\right)$

• No, $\lim_{x\rightarrow2}f\left(x\right)\ne f\left(2\right)$

Tags

CCSS.8.F.A.1

CCSS.HSF.IF.B.5

A function is continuous on a number if and only if f(c) = lim f(x) as x approaches a number c.

• TRUE

• FALSE

Is the function  $f\left(x\right)=x^2-2x+1$ , continuous at x=0?

• yes

• no

Tags

CCSS.HSF.IF.C.7