3. Let lim (2x + a* + e*)1/= L x- 00 which of the following statement(s) is(are) correct? (a) if L = a(a > 0), then the range of a is [e, oo) (b) if L = 2e(a > 0), then the range of a is {2e} (c) if L = e(a > 0), then the range of a is (0, e] (d) if L = 2a (a > 1), then the range of a is

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( 3 lim _{x rightarrow infty}left(2^{x}+a^{x}+e^{x}right)^{1 / x}=L ) ( therefore L=max (2, a, e) ) or ( max (a, e) ) as ( l lambda 2 ) As taking max Ca,e) ismmon flim kadked gives as 1 inside klacket ( therefore quad f_{f} quad b=a, quad therefore ) range ( =[underline{c}, omega) ) ( y=L=2 e, quad a=2 e_{text {sange }}=left{2 e^{2}right} ) ( 4-L=e quad ) if mean ( a leq e ) range ( =(0, c] ) ( y in L=2 a quad ) mams ( a=1 / 2 quad therefore ) range ( ={l} ) : ( quad(A)(B)(C) ) are arsct

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