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`

Prove that lim_(xrarr0) ((1+x)^(n) - 1)/(x) = n .

("lim")_(xtooo)(a n-(1+n^2)/(1+n))=b , where a is a finite number, then(a) a=1 (b) a=0 (c) b=1 (d) b=-1

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

The integer n for which lim_(x->0)((cosx-1)(cosx-e^x))/(x^n) is finite nonzero number is ________

The n t h derivative of x e^x vanishes when (a) x=0 (b) x=-1 (c) x=-n (d) x=n

If |[x^n, x^(n+2),x^(2n)],[1,x^a, a],[x^(n+5),x^(a+6),x^(2n+5)]|=0,AAx in R ,where n in N , then value of a is (a) n (b) n-1 (c) n+1 (d) none of these

If f(x+1)+f(x-1)=2f(x)a n df(0),=0, then f(n),n in N , is nf(1) (b) {f(1)}^n (c) 0 (d) none of these

If f(x)=lim_(n->oo)((x^2+a x+1)+x^(2n)(2x^2+x+b))/(1+x^(2n))and lim_(x->+-1)f(x) exist, then The value of b is (a) -1 (b). 1 ( c.) 0 (d). 2

If X""=""{4^n-3n-1"":""n in N}""a n d""Y""=""{9(n-1)"": n in N} , where N is the set of natural numbers, then XuuY is equal to (1) N (2) Y - X (3) X (4) Y

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