If `f(x)` is differentiable and strictly increasing function, then the value of `("lim")_(xvec0)(f(x^2)-f(x))/(f(x)-f(0))` is 1 (b) 0 (c) `-1` (d) 2

Let f(x) be a twice-differentiable function and f''(0)=2. Then evaluate lim_(xto0) (2f(x)-3f(2x)+f(4x))/(x^(2)).

If f(x)=lim_(nrarroo) (cos(x)/(sqrtn))^(n) , then the value of lim_(xrarr0) (f(x)-1)/(x) is

If y=f(x^3),z=g(x^5),f^(prime)(x)=tanx ,a n dg^(prime)(x)=secx , then find the value of (lim)_(xvec0)(((dy)/(dz)))/x

If f: RvecR be a differen tiable function atg x=0 satisfying f(0)=0a n df^(prime)(0)=1 , then the value of (lim)_(xvec0)1/xsum_(n=1)^oo(-1)^nf(x/n)= e b. -log2 c. 0 d. 1

If 3-((x^2)/(12))lt=f(x)lt=3+((x^3)/9) for all x!=0, then find the value of ("lim")_(xvec0)f(x)

If f(x) is twice differentiable and f^('')(0) = 3 , then lim_(x rarr 0) (2f(x)-3f(2x)+f(4x))/x^(2) is

Given ("lim")_(xvec0)(f(x))/(x^2)=2,w h e r e[dot] denotes the greatest integer function, then (a) ("lim")_(xvec0)[f(x)]=0 (b) ("lim")_(xvec0)[f(x)]=1 (c) ("lim")_(xvec0)[(f(x))/x] does not exist (d) ("lim")_(xvec0)[(f(x))/x] exists

Let f: RvecR be differentiable and strictly increasing function throughout its domain. Statement 1: If |f(x)| is also strictly increasing function, then f(x)=0 has no real roots. Statement 2: When xvecooorvec-oo,f(x)vec0 , but cannot be equal to zero.

Let f(x) be real valued and differentiable function on R such that f(x+y)=(f(x)+f(y))/(1-f(x)dotf(y)) f(0) is equals a. 1 b. 0 c. -1 d. none of these

If ("lim")_(xvec0)[1+x+(f(x))/x]^(1/x)=e^3, then find the value of 1n(("lim")_(xvec0)[1+(f(x))/x]^(1/x))i s____