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jishan
 2 years ago
evaluate lim x>a ( 2 a/x)^tanpia/2x
jishan
 2 years ago
evaluate lim x>a ( 2 a/x)^tanpia/2x

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Zarkon
 2 years ago
Best ResponseYou've already chosen the best response.1take the log and use l'hospitals rule

shubhamsrg
 2 years ago
Best ResponseYou've already chosen the best response.0in (1+ f(x))^(g(x)) , where f(x) >0 and g(x) > inf, mug it up that the final ans is e^( (f(x) g(x) )

jishan
 2 years ago
Best ResponseYou've already chosen the best response.0solve step by step i m not understand.

RolyPoly
 2 years ago
Best ResponseYou've already chosen the best response.0Let \[\large y = ( 2\frac{ a}{x})^{tan\frac{\pi a}{2x}}\]\[\ln\large y = \ln ( 2\frac{ a}{x})^{tan\frac{\pi a}{2x}}\]\[\ln\large y = (tan\frac{\pi a}{2x})\ln( 2\frac{ a}{x})\]Take limit on both sides\[\lim_{x\rightarrow a}(\ln\large y) = \lim_{x\rightarrow a}[(tan\frac{\pi a}{2x})\ln( 2\frac{ a}{x})]\]Evaluate the limit on the right by l'hopital's rule. Then\[ \lim_{x\rightarrow a}( 2\frac{ a}{x})^{tan\frac{\pi a}{2x}} = \lim_{x\rightarrow a} y = e^{\lim_{x\rightarrow a}lny}\], which is e^(the things you get after evaluating that limit)
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