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  • The value of <img alt="\mathrm{\lim _{x \rightarrow 2}(-1)^{|x|}}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7B%5Clim%20_%7Bx%20%5Crightarrow%202%7D%28-1%29%5E%7B%7Cx%7C%7D%7D"

The value of \mathrm{\lim _{x \rightarrow 2}(-1)^{|x|}} is ........(where [.] denotes the greatest integer function)

Option: 1

0


Option: 2

1


Option: 3

-1


Option: 4

Does not exist.


Answers (1)

best_answer

\mathrm{\text { LHL }=\lim _{x \rightarrow 2^{-}}(-1)^{[x]}=\lim _{h \rightarrow 0}(-1)^{[2-k]}=(-1)^1=-1 }

\mathrm{ \text { RHL }=\lim _{x \rightarrow 2+}(-1)^{[x]}=\lim _{h \rightarrow 0}(-1)^{[2+h]}=(-1)^2=1 }

\mathrm{ \therefore \text { LHL }=\text { RHL }}

ie, does not exist.

Hence option 4 is correct.

Posted by

SANGALDEEP SINGH

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