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Learn That A Limit Can Fail To Exist When Behavior Differs From The Right And From The Left

Identity if the limit of $f\left(x\right)$ exists given the LHL (left-hand limit) and RHL (right-hand limit).

$\lim_{x\to c+f\left(x\right)=0}$ Limit Exist

$\lim_{x\to c-f\left(x\right)=0}$ Limit Exist

Identity if the limit of $f\left(x\right)$ exists given the LHL (left-hand limit) and RHL (right-hand limit).

$\lim_{x\to c+f\left(x\right)=5}$ Limit Exist

$\lim_{x\to c-f\left(x\right)=5}$ Limit does not exist

Identity if the limit of $f\left(x\right)$ exists given the LHL (left-hand limit) and RHL (right-hand limit).

$\lim_{x\to c+f\left(x\right)=\infty}$ Limit Exist

$\lim_{x\to c-f\left(x\right)=\infty}$ Limit does not exist

Identity if the limit of $f\left(x\right)$ exists given the LHL (left-hand limit) and RHL (right-hand limit).

$\lim_{x\to c+f\left(x\right)=2}$ Limit Exist

$\lim_{x\to c-f\left(x\right)=2}$ Limit does not exist

Identity if the limit of $f\left(x\right)$ exists given the LHL (left-hand limit) and RHL (right-hand limit).

$\lim_{x\to c+f\left(x\right)=-4}$ Limit Exist

$\lim_{x\to c-f\left(x\right)=\infty}$ Limit does not exist

Identity if the limit of $f\left(x\right)$ exists given the LHL (left-hand limit) and RHL (right-hand limit).

$\lim_{x\to c+f\left(x\right)=1}$ Limit Exist

$\lim_{x\to c-f\left(x\right)=1}$ Limit does not exist

Identity if the limit of $f\left(x\right)$ exists given the LHL (left-hand limit) and RHL (right-hand limit).

$\lim_{x\to c+f\left(x\right)=3}$ Limit Exist

$\lim_{x\to c-\left(f\right)=4}$ Limit does not exist

Identity if the limit of $f\left(x\right)$ exists given the LHL (left-hand limit) and RHL (right-hand limit).

$\lim_{x\to c+f\left(x\right)=-\infty}$ Limit Exist

$\lim_{x\to c-f\left(x\right)=\infty}$ Limit does not exist

Identity if the limit of $f\left(x\right)$ exists given the LHL (left-hand limit) and RHL (right-hand limit).

$\lim_{x\to c+f\left(x\right)=-4}$ Limit Exist

$\lim_{x\to c-f\left(x\right)=4}$ Limit does not exist

Identity if the limit of $f\left(x\right)$ exists given the LHL (left-hand limit) and RHL (right-hand limit).

$\lim_{x\to c+f\left(x\right)=0}$ Limit Exist

$\lim_{x\to c-f\left(x\right)=4}$ Limit does not exist

Questions

Time

Score

Learn That A Limit Can Fail To Exist When Behavior Differs From The Right And From The Left

Identity if the limit of $f\left(x\right)$ exists given the LHL (left-hand limit) and RHL (right-hand limit).

$\lim_{x\to c+f\left(x\right)=0}$ Limit Exist

$\lim_{x\to c-f\left(x\right)=0}$ Limit Exist

Identity if the limit of $f\left(x\right)$ exists given the LHL (left-hand limit) and RHL (right-hand limit).

$\lim_{x\to c+f\left(x\right)=5}$ Limit Exist

$\lim_{x\to c-f\left(x\right)=5}$ Limit does not exist

Identity if the limit of $f\left(x\right)$ exists given the LHL (left-hand limit) and RHL (right-hand limit).

$\lim_{x\to c+f\left(x\right)=\infty}$ Limit Exist

$\lim_{x\to c-f\left(x\right)=\infty}$ Limit does not exist

Identity if the limit of $f\left(x\right)$ exists given the LHL (left-hand limit) and RHL (right-hand limit).

$\lim_{x\to c+f\left(x\right)=2}$ Limit Exist

$\lim_{x\to c-f\left(x\right)=2}$ Limit does not exist

Identity if the limit of $f\left(x\right)$ exists given the LHL (left-hand limit) and RHL (right-hand limit).

$\lim_{x\to c+f\left(x\right)=-4}$ Limit Exist

$\lim_{x\to c-f\left(x\right)=\infty}$ Limit does not exist

Identity if the limit of $f\left(x\right)$ exists given the LHL (left-hand limit) and RHL (right-hand limit).

$\lim_{x\to c+f\left(x\right)=1}$ Limit Exist

$\lim_{x\to c-f\left(x\right)=1}$ Limit does not exist

Identity if the limit of $f\left(x\right)$ exists given the LHL (left-hand limit) and RHL (right-hand limit).

$\lim_{x\to c+f\left(x\right)=3}$ Limit Exist

$\lim_{x\to c-\left(f\right)=4}$ Limit does not exist

Identity if the limit of $f\left(x\right)$ exists given the LHL (left-hand limit) and RHL (right-hand limit).

$\lim_{x\to c+f\left(x\right)=-\infty}$ Limit Exist

$\lim_{x\to c-f\left(x\right)=\infty}$ Limit does not exist

Identity if the limit of $f\left(x\right)$ exists given the LHL (left-hand limit) and RHL (right-hand limit).

$\lim_{x\to c+f\left(x\right)=-4}$ Limit Exist

$\lim_{x\to c-f\left(x\right)=4}$ Limit does not exist

Identity if the limit of $f\left(x\right)$ exists given the LHL (left-hand limit) and RHL (right-hand limit).

$\lim_{x\to c+f\left(x\right)=0}$ Limit Exist

$\lim_{x\to c-f\left(x\right)=4}$ Limit does not exist

Incorrect

Great!

Questions

Time

Score

Learn That A Limit Can Fail To Exist When Behavior Differs From The Right And From The Left

Identity if the limit of ﻿f(x)f\left(x\right)f(x)﻿ exists given the LHL (left-hand limit) and RHL (right-hand limit).

﻿lim⁡x→c+f(x)=0\lim_{x\to c+f\left(x\right)=0}limx→c+f(x)=0​﻿ Limit Exist

﻿lim⁡x→c−f(x)=0\lim_{x\to c-f\left(x\right)=0}limx→c−f(x)=0​﻿ Limit Exist

Identity if the limit of ﻿f(x)f\left(x\right)f(x)﻿ exists given the LHL (left-hand limit) and RHL (right-hand limit).

﻿lim⁡x→c+f(x)=5\lim_{x\to c+f\left(x\right)=5}limx→c+f(x)=5​﻿ Limit Exist

﻿lim⁡x→c−f(x)=5\lim_{x\to c-f\left(x\right)=5}limx→c−f(x)=5​﻿ Limit does not exist

Identity if the limit of ﻿f(x)f\left(x\right)f(x)﻿ exists given the LHL (left-hand limit) and RHL (right-hand limit).

﻿lim⁡x→c+f(x)=∞\lim_{x\to c+f\left(x\right)=\infty}limx→c+f(x)=∞​﻿ Limit Exist

﻿lim⁡x→c−f(x)=∞\lim_{x\to c-f\left(x\right)=\infty}limx→c−f(x)=∞​﻿ Limit does not exist

Identity if the limit of ﻿f(x)f\left(x\right)f(x)﻿ exists given the LHL (left-hand limit) and RHL (right-hand limit).

﻿lim⁡x→c+f(x)=2\lim_{x\to c+f\left(x\right)=2}limx→c+f(x)=2​﻿ Limit Exist

﻿lim⁡x→c−f(x)=2\lim_{x\to c-f\left(x\right)=2}limx→c−f(x)=2​﻿ Limit does not exist

Identity if the limit of ﻿f(x)f\left(x\right)f(x)﻿ exists given the LHL (left-hand limit) and RHL (right-hand limit).

﻿lim⁡x→c+f(x)=−4\lim_{x\to c+f\left(x\right)=-4}limx→c+f(x)=−4​﻿ Limit Exist

﻿lim⁡x→c−f(x)=∞\lim_{x\to c-f\left(x\right)=\infty}limx→c−f(x)=∞​﻿ Limit does not exist

Identity if the limit of ﻿f(x)f\left(x\right)f(x)﻿ exists given the LHL (left-hand limit) and RHL (right-hand limit).

﻿lim⁡x→c+f(x)=1\lim_{x\to c+f\left(x\right)=1}limx→c+f(x)=1​﻿ Limit Exist

﻿lim⁡x→c−f(x)=1\lim_{x\to c-f\left(x\right)=1}limx→c−f(x)=1​﻿ Limit does not exist

Identity if the limit of ﻿f(x)f\left(x\right)f(x)﻿ exists given the LHL (left-hand limit) and RHL (right-hand limit).

﻿lim⁡x→c+f(x)=3\lim_{x\to c+f\left(x\right)=3}limx→c+f(x)=3​﻿ Limit Exist

﻿lim⁡x→c−(f)=4\lim_{x\to c-\left(f\right)=4}limx→c−(f)=4​﻿ Limit does not exist

Identity if the limit of ﻿f(x)f\left(x\right)f(x)﻿ exists given the LHL (left-hand limit) and RHL (right-hand limit).

﻿lim⁡x→c+f(x)=−∞\lim_{x\to c+f\left(x\right)=-\infty}limx→c+f(x)=−∞​﻿ Limit Exist

﻿lim⁡x→c−f(x)=∞\lim_{x\to c-f\left(x\right)=\infty}limx→c−f(x)=∞​﻿ Limit does not exist

Identity if the limit of ﻿f(x)f\left(x\right)f(x)﻿ exists given the LHL (left-hand limit) and RHL (right-hand limit).

﻿lim⁡x→c+f(x)=−4\lim_{x\to c+f\left(x\right)=-4}limx→c+f(x)=−4​﻿ Limit Exist

﻿lim⁡x→c−f(x)=4\lim_{x\to c-f\left(x\right)=4}limx→c−f(x)=4​﻿ Limit does not exist

Identity if the limit of ﻿f(x)f\left(x\right)f(x)﻿ exists given the LHL (left-hand limit) and RHL (right-hand limit).

﻿lim⁡x→c+f(x)=0\lim_{x\to c+f\left(x\right)=0}limx→c+f(x)=0​﻿ Limit Exist

﻿lim⁡x→c−f(x)=4\lim_{x\to c-f\left(x\right)=4}limx→c−f(x)=4​﻿ Limit does not exist

Incorrect

Great!

Identity if the limit of $f\left(x\right)$ exists given the LHL (left-hand limit) and RHL (right-hand limit).

$\lim_{x\to c+f\left(x\right)=0}$ Limit Exist

$\lim_{x\to c-f\left(x\right)=0}$ Limit Exist

Identity if the limit of $f\left(x\right)$ exists given the LHL (left-hand limit) and RHL (right-hand limit).

$\lim_{x\to c+f\left(x\right)=5}$ Limit Exist

$\lim_{x\to c-f\left(x\right)=5}$ Limit does not exist

Identity if the limit of $f\left(x\right)$ exists given the LHL (left-hand limit) and RHL (right-hand limit).

$\lim_{x\to c+f\left(x\right)=\infty}$ Limit Exist

$\lim_{x\to c-f\left(x\right)=\infty}$ Limit does not exist

Identity if the limit of $f\left(x\right)$ exists given the LHL (left-hand limit) and RHL (right-hand limit).

$\lim_{x\to c+f\left(x\right)=2}$ Limit Exist

$\lim_{x\to c-f\left(x\right)=2}$ Limit does not exist

Identity if the limit of $f\left(x\right)$ exists given the LHL (left-hand limit) and RHL (right-hand limit).

$\lim_{x\to c+f\left(x\right)=-4}$ Limit Exist

$\lim_{x\to c-f\left(x\right)=\infty}$ Limit does not exist

Identity if the limit of $f\left(x\right)$ exists given the LHL (left-hand limit) and RHL (right-hand limit).

$\lim_{x\to c+f\left(x\right)=1}$ Limit Exist

$\lim_{x\to c-f\left(x\right)=1}$ Limit does not exist

Identity if the limit of $f\left(x\right)$ exists given the LHL (left-hand limit) and RHL (right-hand limit).

$\lim_{x\to c+f\left(x\right)=3}$ Limit Exist

$\lim_{x\to c-\left(f\right)=4}$ Limit does not exist

Identity if the limit of $f\left(x\right)$ exists given the LHL (left-hand limit) and RHL (right-hand limit).

$\lim_{x\to c+f\left(x\right)=-\infty}$ Limit Exist

$\lim_{x\to c-f\left(x\right)=\infty}$ Limit does not exist

Identity if the limit of $f\left(x\right)$ exists given the LHL (left-hand limit) and RHL (right-hand limit).

$\lim_{x\to c+f\left(x\right)=-4}$ Limit Exist

$\lim_{x\to c-f\left(x\right)=4}$ Limit does not exist

Identity if the limit of $f\left(x\right)$ exists given the LHL (left-hand limit) and RHL (right-hand limit).

$\lim_{x\to c+f\left(x\right)=0}$ Limit Exist

$\lim_{x\to c-f\left(x\right)=4}$ Limit does not exist