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  • <img alt="\text { Let f(x)}=\left\{\begin{array}{cc} \mathrm{\left(\left(e^{[x]}-e^{[x]}\right) e^{-x}+A\right),} & \mathrm{x<0}\\ \mathrm{\frac{2 \sin \{x]}{\tan \{x]} }& , \mathrm{ xg

\text { Let f(x)}=\left\{\begin{array}{cc} \mathrm{\left(\left(e^{[x]}-e^{[x]}\right) e^{-x}+A\right),} & \mathrm{x<0}\\ \mathrm{\frac{2 \sin \{x]}{\tan \{x]} }& , \mathrm{ x>0} \\ 2 & , \mathrm{ x=0} \end{array}\right.

The value of A so that f is continuous at x=0 is ([x] is greatest integer function and |x| is the fractional part of x is
 

Option: 1

\mathrm{e^{-1}}


Option: 2

\mathrm{ 3-e^{-1}}


Option: 3

\mathrm{2-e^{-1}}


Option: 4

2


Answers (1)

best_answer

\begin{aligned} & \mathrm{\left.f(0)=2 \text { and } \lim _{x \rightarrow 0-} f(x)=\lim _{x \rightarrow+\infty}\left(e^{[x]}-e^{\{x\}}\right) e^{-x}+\mathrm{A}\right)} \\ &\mathrm{ =\left(e^{-1}-1\right)+\mathrm{A} }\end{aligned}

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Irshad Anwar

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