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  • <img alt="\mathrm{\lim _{x \rightarrow 2} \frac{(\cos \alpha)^x+(\sin \alpha)^x-1}{x-2}}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7B%5Clim%20_%7Bx%20%5Crightarrow%202%7D%20%5

\mathrm{\lim _{x \rightarrow 2} \frac{(\cos \alpha)^x+(\sin \alpha)^x-1}{x-2}} is equal to

Option: 1

\infty


Option: 2

(\cos \alpha)^2+(\sin \alpha)^2


Option: 3

0


Option: 4

none of these


Answers (1)

best_answer

\mathrm{\lim _{x \rightarrow 2} \frac{(\cos \alpha)^x+(\sin \alpha)^x-1}{x-2}=\lim _{x \rightarrow 2} \frac{(\cos \alpha)^x \log _e(\cos \alpha)+(\sin \alpha)^x \log _e(\sin \alpha)}{1}}
 

Using L'Hospital rule

\mathrm{=\cos ^2 \alpha\left(\log _e \cos \alpha\right)+\sin ^2 \alpha \log _e(\sin \alpha)}

Posted by

jitender.kumar

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