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Calculus 2 : Limits and Continuity

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Example Question #11 : Limits And Continuity

Screen shot 2015 08 18 at 10.00.45 am

Given the above graph of f(x) , over which of the following intervals is f(x) continuous?

Possible Answers:

$(-\infty,-2)\cup(-2,1)\cup(1,\infty)$

$(-\infty,0)\cup(0,2)\cup(2,\infty)$

$(-\infty,-2)\cup(-2,2)\cup(2,\infty)$

$(-\infty,-2)\cup(-2,0)\cup(0,\infty)$

$(-\infty,0)\cup(0,1)\cup(1,\infty)$

Correct answer:

$(-\infty,0)\cup(0,2)\cup(2,\infty)$

Explanation:

For a function f(x) to be continuous at a given point (a, f(a)) , it must meet the following two conditions:

1.) The point (a, f(a)) must exist, and

2.) $\lim_{x\rightarrow a}f(x)=f(a)$ .

Examining the above graph, f(x) is continuous at every possible value of except for x=0 and x=2 . Thus, f(x) is continuous on the interval $(-\infty,0)\cup(0,2)\cup(2,\infty)$ .

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Example Question #12 : Limits And Continuity

Screen shot 2015 08 18 at 11.04.49 am

Given the above graph of f(x) , over which of the following intervals is f(x) continuous?

Possible Answers:

$(-\infty,1)\cup(1,\infty)$

$(-\infty,-\frac{1}2{})\cup(-\frac{1}{2},\infty)$

$(-\infty,0)\cup(0,\infty)$

$(-\infty,2)\cup(2,\infty)$

$(-\infty,-1)\cup(-1,\infty)$

Correct answer:

$(-\infty,-1)\cup(-1,\infty)$

Explanation:

For a function f(x) to be continuous at a given point (a, f(a)) , it must meet the following two conditions:

1.) The point (a, f(a)) must exist, and

2.) $\lim_{x\rightarrow a}f(x)=f(a)$ .

Examining the above graph, f(x) is continuous at every possible value of except for x=-1 . Thus, f(x) is continuous on the interval $(-\infty,-1)\cup(-1,\infty)$ .

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Example Question #11 : Limits And Continuity

Screen shot 2015 08 19 at 1.42.40 pm

Given the above graph of f(x) , over which of the following intervals is f(x) continuous?

Possible Answers:

$(-\infty,11)\cup(11,\infty)$

$(-\infty,-11)\cup(-11,11)\cup(11,\infty)$

$(-\infty,0)\cup(0,\infty)$

$(-\infty,-11)\cup(-11,\infty)$

$(-\infty,0)\cup(0,11)\cup(11,\infty)$

Correct answer:

$(-\infty,11)\cup(11,\infty)$

Explanation:

For a function f(x) to be continuous at a given point (a, f(a)) , it must meet the following two conditions:

1.) The point (a, f(a)) must exist, and

2.) $\lim_{x\rightarrow a}f(x)=f(a)$ .

Examining the above graph, f(x) is continuous at every possible value of except for x=11 . Thus, f(x) is continuous on the interval $(-\infty,11)\cup(11,\infty)$ .

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Example Question #11 : Limits And Continuity

Screen shot 2015 08 19 at 2.31.48 pm

Given the above graph of f(x) , over which of the following intervals is f(x) continuous?

Possible Answers:

$(-\infty,1)\cup(1,\infty)$

$(-\infty,-2)\cup(-2,\infty)$

$(-\infty,0)\cup(0,\infty)$

$(-\infty,-2)\cup(-2,2)\cup(2,\infty)$

$(-\infty,2)\cup(2,\infty)$

Correct answer:

$(-\infty,2)\cup(2,\infty)$

Explanation:

For a function f(x) to be continuous at a given point (a, f(a)) , it must meet the following two conditions:

1.) The point (a, f(a)) must exist, and

2.) $\lim_{x\rightarrow a}f(x)=f(a)$ .

Examining the above graph, f(x) is continuous at every possible value of except for x=2 . Thus, f(x) is continuous on the interval $(-\infty,2)\cup(2,\infty)$ .

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Example Question #15 : Limits And Continuity

Screen shot 2015 08 19 at 2.44.53 pm

Given the above graph of f(x) , over which of the following intervals is f(x) continuous?

Possible Answers:

$(-\infty,-5)\cup(-5,5)\cup(5,\infty)$

$(-\infty,5)\cup(5,\infty)$

$(-\infty,0)\cup(0,5)\cup(5,\infty)$

$(-\infty,-1)\cup(-1,0)\cup(0,\infty)$

$(-\infty,-5)\cup(-5,\infty)$

Correct answer:

$(-\infty,5)\cup(5,\infty)$

Explanation:

For a function f(x) to be continuous at a given point (a, f(a)) , it must meet the following two conditions:

1.) The point (a, f(a)) must exist, and

2.) $\lim_{x\rightarrow a}f(x)=f(a)$ .

Examining the above graph, f(x) is continuous at every possible value of except for x=5 . Thus, f(x) is continuous on the interval $(-\infty,5)\cup(5,\infty)$ .

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Example Question #16 : Limits And Continuity

Screen shot 2015 08 19 at 4.51.39 pm

Given the above graph of f(x) , over which of the following intervals is f(x) continuous?

Possible Answers:

$(-\infty,-\frac{1}{2})\cup\(-\frac{1}{2},0)\cup(0,\frac{1}{2})\cup(\frac{1}{2},\infty)$

$(-\infty,-2)\cup\(-2,0)\cup(0,2)\cup(2,\infty)$

$(-\infty,-1)\cup\(-1,1)\cup(1,\infty)$

$(-\infty,-1)\cup\(-1,0)\cup(0,1)\cup(1,\infty)$

$(-\infty,0)\cup(0,1)\cup(1,\infty)$

Correct answer:

$(-\infty,-1)\cup\(-1,0)\cup(0,1)\cup(1,\infty)$

Explanation:

For a function f(x) to be continuous at a given point (a, f(a)) , it must meet the following two conditions:

1.) The point (a, f(a)) must exist, and

2.) $\lim_{x\rightarrow a}f(x)=f(a)$ .

Examining the above graph, f(x) is continuous at every possible value of except for x=-1 , x=0 , and x=1 . Thus, f(x) is continuous on the interval $(-\infty,-1)\cup\(-1,0)\cup(0,1)\cup(1,\infty)$ .

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Example Question #11 : Limits And Continuity

Screen shot 2015 08 19 at 5.23.24 pm

Given the above graph of f(x) , over which of the following intervals is f(x) continuous?

Possible Answers:

$(-\infty,0)\cup(0,\infty)$

$(-\infty,-1)\cup(-1,\infty)$

$(-\infty,1)\cup(1,\infty)$

$(-\infty,-2)\cup(-2,0)\cup(0,\infty)$

$(-\infty,2)\cup(2,\infty)$

Correct answer:

$(-\infty,0)\cup(0,\infty)$

Explanation:

For a function f(x) to be continuous at a given point (a, f(a)) , it must meet the following two conditions:

1.) The point (a, f(a)) must exist, and

2.) $\lim_{x\rightarrow a}f(x)=f(a)$ .

Examining the above graph, f(x) is continuous at every possible value of except for , x=0 . Thus, f(x) is continuous on the interval $(-\infty,0)\cup(0,\infty)$ .

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Example Question #18 : Limits And Continuity

Screen shot 2015 08 19 at 5.43.00 pm

Given the above graph of f(x) , over which of the following intervals is f(x) continuous?

Possible Answers:

$(-\infty,-3)\cup(-3,\infty)$

$(-\infty,-4)\cup(-4,\infty)$

$(-\infty,0)\cup(0,\infty)$

$(-\infty,-1)\cup(-1,\infty)$

$(-\infty,-2)\cup(-2,\infty)$

Correct answer:

$(-\infty,-3)\cup(-3,\infty)$

Explanation:

For a function f(x) to be continuous at a given point (a, f(a)) , it must meet the following two conditions:

1.) The point (a, f(a)) must exist, and

2.) $\lim_{x\rightarrow a}f(x)=f(a)$ .

Examining the above graph, f(x) is continuous at every possible value of except for , x=-3 . Thus, f(x) is continuous on the interval $(-\infty,-3)\cup(-3,\infty)$ .

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Example Question #19 : Limits And Continuity

Screen shot 2015 08 21 at 11.18.01 am

Given the above graph of f(x) , over which of the following intervals is f(x) continuous?

Possible Answers:

$(1,\infty)$

$(-\infty,0)\cup(0,\infty)$

$(-\infty,1)\cup(1,\infty)$

$(0,\infty)$

$(-\infty,0)$

Correct answer:

$(0,\infty)$

Explanation:

For a function f(x) to be continuous at a given point (a, f(a)) , it must meet the following two conditions:

1.) The point (a, f(a)) must exist, and

2.) $\lim_{x\rightarrow a}f(x)=f(a)$ .

Examining the above graph, f(x) is continuous at every possible value of except for $x\leq0$ . Thus, f(x) is continuous on the interval $(0,\infty)$ .

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Calculus 2 : Limits and Continuity

Study concepts, example questions & explanations for Calculus 2

All Calculus 2 Resources

Example Questions

Example Question #11 : Limits And Continuity

Example Question #12 : Limits And Continuity

Example Question #11 : Limits And Continuity

Example Question #11 : Limits And Continuity

Example Question #15 : Limits And Continuity

Example Question #16 : Limits And Continuity

Example Question #11 : Limits And Continuity

Example Question #18 : Limits And Continuity

Example Question #19 : Limits And Continuity

All Calculus 2 Resources

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