`lim_(x->0)` `(sinx^n)/((sinx)^m),(mltn),` is equal to (a) 1 (b) 0 (c) `n//m` (d) none of these

lim_(xrarr0) (x^(2)-x)/(sinx)

If y=tan^(-1)((sinx+cosx)/(cosx-sinx)) , then (dy)/(dx) is equal to (a) 1/2 (b) 0 (c) 1 (d) none of these

If m,n inN,lim_(xto0) (sinx^(n))/((sinx)^(m)) is

("lim")_(x -> 0)((1+tanx)/(1+sinx))^(cos e cx) is equal to (a)e (b) 1/e (c) 1 (d) none of these

lim_(xrarr0+) (sinsqrt(x))/(sqrt(sinx)) is equal to

If f(x)=((x^l)/(x^m))^(l+m)((x^m)/(x^n))^(m+n)((x^n)/(x^l))^(n+l) , then f^(prime)(x) is equal to (a) 1 (b) 0 (c) x^(l+m+n) (d) none of these

lim_(xto0) ((1+tanx)/(1+sinx))^(cosecx) is equal to

lim_(xrarr0) (sinx)/(x)= ?

If mgt0, ngt0 , the definite integral I=int_0^1 x^(m-1)(1-x)^(n-1)dx depends upon the values of m and n is denoted by beta(m,n) , called the beta function.Obviously, beta(n,m)=beta(m,n) .Now answer the question:If int_0^oo x^(m-1)/(1+x)^(m+n)dx=k int_0^oo x^(n-1)/(1+x)^(m+n)dx , then k is equal to (A) m/n (B) 1 (C) n/m (D) none of these

lim_(x->0) (2e^sinx-e^(-sinx)-1)/(x^2+2x)