The Limiting limit

Calculus Level pending

Answer the question number 4. Try not to use L'Hôpital's Rule P.S. I have written a doubt in solution section please help me with it if you can.

Moderator's edit:

Find the value of \(\alpha\) for wihch the functiion \(f(x) \) is defined as

\[ f(x) = \begin{cases} \alpha \sin \dfrac{\pi}2 (x+1) , \qquad x \leq 0 \\ \dfrac{\tan x - \sin x}{x^3} , \qquad x> 0 \end{cases} \]

and is continuous at \(x=0 \).


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