If `f(a)=(1)/(4)`, then `underset(hrarr0)(lim)(f(a+2h^(2))-f(a-2h^(2)))/(f(a+h^(3)-h^(2))-f(a-h^(3)+h^(2)))`=

If f(a)=(1)/(4) , then lim_(hrarr0) (f(a+2h^(2))-f(a-2h^(2)))/(f(a+h^(3)-h^(2))-f(a-h^(3)+h^(2))) =

Evaluate underset (h to 0) lim ((a+h)^(2) sin (a+h) -a^(2) sin a)/h .

Evaluate lim_(hto0) (log_(e)(1+2h)-2log_(e)(1+h))/(h^(2)).

If f(x)=log((1+x)/(1-x)),t h e n (a) f(x_1)f(x)=f(x_1+x_2) (b) f(x+2)-2f(x+1)+f(x)=0 (c) f(x)+f(x+1)=f(x^2+x) (d) f(x_1)+f(x_2)=f((x_1+x_2)/(1+x_1x_2))

If f(0)=1,f(2)=3,f(2)=5,t h e nfin dt h ev a l u eof int_0^1xf"(2x)dx

Let f:RrarrR be such that f(a)=1, f(a)=2 . Then lim_(x to 0)((f^(2)(a+x))/(f(a)))^(1//x) is

If f(x)=x^3-x^2+100x+2002 ,t h e n f(1000)>f(1001) f(1/(2000))>f(1/(2001)) f(x-1)>f(x-2) f(2x-3)>f(2x)

Suppose that F(x) is an anti-derivative of f(x)=(sinx)/x ,w h e r ex > 0. Then int_1^3(sin2x)/xdx can be expressed as (a) F(6)-F(2) (b) 1/2(F(6)-f(2)) (c) 1/2(F(3)-f(1)) (d) 2(F(6))-F(2))

If f(x)=1/x ,g(x)=1/(x^2), and h(x)=x^2 , then (A) f(g(x))=x^2,x!=0,h(g(x))=1/(x^2) (B) h(g(x))=1/(x^2),x!=0,fog(x)=x^2 (C) fog(x)=x^2,x!=0,h(g(x))=(g(x))^2,x!=0 (D) none of these

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