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

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

"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

(lim)_(xrarr0)(sin(picos^2x)/(x^2)) is equal to (a) -pi (b) pi (c) pi/2 (d) 1

If lim_(x->0)(x^n-sinx^n)/(x-sin^n x) is non-zero finite, then n must be equal to (a) 4 (b) 1 (c) 2 (d) 3

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 lim_(x->0)(x^n-sinx^n)/(x-sin^n x) is non-zero finite, then n must be equal to 4 (b) 1 (c) 2 (d) 3

Let F(x)=int_(sinx)^(cosx)e^((1+sin^(-1)(t))dt on [0,(pi)/(2)] , then

Let function f be defined as f:R^(+)toR^(+) and function g is defined as g:R^(+)toR^(+) . Functions f and g are continuous in their domain. Suppose, the function h(x)=lim_(ntooo)(x^(n)f(x)+x^(2))/(x^(n)+g(x)), x gt0 . If h(x) is continuous in its domain,then f(1).g(1) is equal to (a) 2 (b) 1 (c) 1/2 (d) 0

Let f(x) = secx*f'(x), f(0) = 1, then f(pi/6) is equal to