Let `f(x)=(lim)_(h->0)(("sin"(x+h))^(1n(x+h))-(sinx)^(1nx))/hdot` Then `f(pi/2)` equal to (a)0 (b) equal to 1 (c)In `pi/2` (d) non-existent

Let f(x)=lT_(h rarr0)(sin(x+h)^(In(x+h))-(sin x)^(In x))/(h) then f((pi)/(2)) is

Q.Let f(x)=lim_(x rarr0)(((sin(x+h))^(ln(x+h))-(sin x)^(ln x))/(h)) then the value of f((pi)/(2)) is

"If "f(x)=lim_(hrarr0) ((sin(x+h))^(log_(e)(x+h))-(sin x)^(log_(e)x))/(h)" then find "f(pi//2).

f(x)=(1n(x^2+e^x))/(1n(x^4+e^(2x)))dotT h e n lim_(x->oo)f(x) is equal to (a) 1 (b) 1/2 (c) 2 (d) none of these

D*f(x)=lim_(h rarr0)(f^(2)(x+h)-f^(2)(x))/(h) If f(x)=x ln x then D*f(x) at x=e equals

Let f(x)=(sqrt(1+sinx)-sqrt(1-sinx))/(tanx) , x ne 0 Then lim_(x to 0) f(x) is equal to

lim_(x rarr oo)(1)/(1+n sin^(2)nx)is equal to -1 (b) 0 (c) 1 (d) oo

If f(x)= int_(0^(sinx) cos^(-1)t dt +int_(0)^(cosx) sin^(-1)t dt, 0 lt x lt (pi)/(2) then f(pi//4) is equal to

If f(x)=0 is a quadratic equation such that f(-pi)=f(pi)=0 and f((pi)/(2))=-(3 pi^(2))/(4) then lim_(x rarr-pi)(f(x))/(sin(sin x)) is equal to (a)0( b) pi (c) 2 pi (d) none of these