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  •  Find the points of discontinuity of the following functions. <img alt="\mathrm{f(x)=\frac{1}{1-e^{\frac{x-2}{x-3}}}}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7Bf

 Find the points of discontinuity of the following functions.
\mathrm{f(x)=\frac{1}{1-e^{\frac{x-2}{x-3}}}}

Option: 1

\mathrm{f(x)} is continuous for all \mathrm{x}.
 


Option: 2

\mathrm{f(x)}is not continuous for all \mathrm{x}.


Option: 3

\mathrm{f(x)} is not continuous at \mathrm{x=2} and \mathrm{x=3}

 


Option: 4

 NOTA


Answers (1)

best_answer

\begin{aligned} &\mathrm{ f(x)=\frac{1}{1-e^{\frac{x-2}{x-3}}} }\\ &\mathrm{ \text { Here, } \frac{x-2}{x-3} \text { so, } x \neq 3 }\\ &\mathrm{ 1-e^{\frac{x-2}{x-3}} \neq 0 \text { so, } 1 \neq e^{\frac{x-2}{x-3}} }\\ &\mathrm{ e^0 \neq e^{\frac{x-2}{x-3}} \text { so, } 0 \propto \frac{x-2}{x-3} }\\ &\mathrm{Thus, \quad x \neq 2}\\ &\text{hes f(x) is not continuous at x=2 and x=3.}\\ \end{aligned}

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