The value of lim x - 0-x-x is

The correct option is C Does not existLHL=lim _h→ 0|0 h|/0 h =lim _h→ 0h/ h= 1 RHL=lim _h→ 0|0+h|/0+h =lim _h→ 0h/h=1 LHL≠RHL ∴ Limit does not exist at x=0. ...

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Standard XII

Mathematics

Standard Limits to Remove Indeterminate Form

The value of ...

Question

The value of $lim x \to 0 \frac{| x |}{x}$ is

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-1

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0.0

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Does not exist

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Solution

The correct option is D Does not exist
LHL $= lim h \to 0 \frac{| 0 - h |}{0 - h} = lim h \to 0 \frac{h}{- h} = - 1$
RHL $= lim h \to 0 \frac{| 0 + h |}{0 + h} = lim h \to 0 \frac{h}{h} = 1$

LHL $\neq$ RHL
$∴$ Limit does not exist at $x = 0$ .

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The value of limx→0|x|x is

The correct option is D Does not existLHL=limh→0|0−h|0−h=limh→0h−h=−1 RHL=limh→0|0+h|0+h=limh→0hh=1 LHL≠RHL ∴ Limit does not exist at x=0.

The value of $lim x \to 0 \frac{| x |}{x}$ is

The correct option is D Does not exist
LHL $= lim h \to 0 \frac{| 0 - h |}{0 - h} = lim h \to 0 \frac{h}{- h} = - 1$
RHL $= lim h \to 0 \frac{| 0 + h |}{0 + h} = lim h \to 0 \frac{h}{h} = 1$

LHL $\neq$ RHL
$∴$ Limit does not exist at $x = 0$ .