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)=(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 sinx+cos e cx=2, then sin^n x+cos e c^n x is equal to 2 (b) 2^n (c) 2^(n-1) (d) 2^(n-2)

If ("lim")_(xrarr0)({(a-n)n x-tanx}sinn x)/(x^2)=0, where n is nonzero real number, the a is 0 (b) (n+1)/n (c) n (d) n+1/n

If the graph of the function f(x)=(a^x-1)/(x^n(a^x+1)) is symmetrical about the y-a xi s ,then n equals 2 (b) 2/3 (c) 1/4 (d) 1/3

If the equation (4cos^(2)x -2 sinx -3 ) sin x, then x is equal to (n in Z)

lim_(nrarroo) (1-x+x.root n e)^(n) is equal to

lim_(x->0)((1^x+2^x+...........+n^x)/n)^(1/x) is equal to

The value of lim_(x->oo)((2^(x^n))^(1/e^x)-(3^(x^n))^(1/e^x))/(x^n) (where n in N) is (a) logn(2/3) (b) 0 (c) nlogn(2/3) (d) none of defined

If ("lim")_(xvec0)(cos4x+acos2x+b)/(x^4) is finite, find aa n db using expansion formula.

If the period of (cos(sin(n x)))/(tan(x/n)),n in N ,i s6pi , then n= (a) 3 (b) 2 (c) 6 (d) 1