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  • Let the function <img alt="\mathrm{f(x)=\left\{\begin{array}{cl}\frac{\log _{e}(1+5 x)-\log _{e}(1+\alpha x)}{x} & \text { if } x \neq 0 \\ 10 & \text { if } x=0\end{array}\right.}" src="/l

Let the function \mathrm{f(x)=\left\{\begin{array}{cl}\frac{\log _{e}(1+5 x)-\log _{e}(1+\alpha x)}{x} & \text { if } x \neq 0 \\ 10 & \text { if } x=0\end{array}\right.}  be continuous at \mathrm{x=0}. Then \mathrm{\alpha} is equal to

Option: 1

10


Option: 2

-10


Option: 3

5


Option: 4

-5


Answers (1)

best_answer

\begin{aligned} &\text { For continuous at } x=0 \\ &\mathrm{\lim _{x \rightarrow 0}\left(\frac{\log (1+5 x)}{x}-\frac{\log (1+\alpha x)}{\alpha}\right)=10} \\ &\Rightarrow \mathrm{5-\alpha=10} \\ &\Rightarrow \mathrm{\alpha=-5} \end{aligned}

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Devendra Khairwa

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