If `f(9)=9,f^(prime)(9)=4,t h e n("lim")_(x->9)(sqrtf(x)-3)/(sqrtx-3)=` ___________.

(x-3)/(x^(2)-9)=___ .

Find Lim_(x rarr0) (sqrt(t^2+9)-3)/(t^2)

If y=f(x) is an odd differentiable function defined on (-oo,oo) such that f^(prime)(3)=-2,t h e n|f^(prime)(-3)| equals_________.

Let f: R->R be such that f(1)=3a n df^(prime)(1)=6. Then lim_(x->0)((f(1+x))/(f(1)))^(1//x)= (a) 1 (b) e^(1/2) (c) e^2 (d) e^3

9 x e ^(3x)

Suppose the function f(x) satisfies the relation f(x+y^3)=f(x)+f(y^3)dotAAx ,y in R and is differentiable for all xdot Statement 1: If f^(prime)(2)=a ,t h e nf^(prime)(-2)=a Statement 2: f(x) is an odd function.

Evaluate : lim_(xrarr0)[sqrt(x^2 +16) -4]/[sqrt(x^2 +9)-3]

If f(1)=3,f^(prime)(1)=2,f''(1)=4,t h e n f^(-1)(3)= a. 1 b. -1/2 c. -2 d. none of these

lim_(xto3)(x^(2)-9)/(x^(2)(x^(2)-6x+9))

If u=f(x^3),v=g(x^2),f^(prime)(x)=cosx ,a n dg^(prime)(x)=sinx ,t h e n(d u)/(d v) is