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

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jishan
 one year ago
Best ResponseYou've already chosen the best response.0zarkon brother help me.

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

shubhamsrg
 one year 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
 one year ago
Best ResponseYou've already chosen the best response.0solve step by step i m not understand.

RolyPoly
 one year 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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