Let f(x) is a function continuous for all `x in R`except at `x=0` such that `f'(x) <0 AA x in (-oo, 0)` and` f'(x)>0 AA x in(0,oo)`. If `lim_(x->0^+) f (x)= 3`, `lim_(x->0^-) f(x)= 4` and f (0) 5, then the image of the point (0,1) about the line `ylim_(x->0) f(cos^3 x -cos^2x)= xlim_(x->0) f( sin^2 x- sin^3 x)`, is

Let f(x) is a function continuous for all x in R except at x = 0 such that f'(x) lt 0, AA x in (-oo, 0) and f'(x) gt 0, AA x in (0, oo) . If lim_(x rarr 0^(+)) f(x) = 3, lim_(x rarr 0^(-)) f(x) = 4 and f(0) = 5 , then the image of the point (0, 1) about the line, y.lim_(x rarr 0) f(cos^(3) x - cos^(2) x) = x. lim_(x rarr 0) f(sin^(2) x - sin^(3) x) , is

Let f(x) is a function continuous for all x in R except at x = 0 such that f'(x) lt 0, AA x in (-oo, 0) and f'(x) gt 0, AA x in (0, oo) . If lim_(x rarr 0^(+)) f(x) = 3, lim_(x rarr 0^(-)) f(x) = 4 and f(0) = 5 , then the image of the point (0, 1) about the line, y.lim_(x rarr 0) f(cos^(3) x - cos^(2) x) = x. lim_(x rarr 0) f(sin^(2) x - sin^(3) x) , is

Let f(x) is a function continuous for all x in R except at x = 0 such that f'(x) lt 0, AA x in (-oo, 0) and f'(x) gt 0, AA x in (0, oo) . If lim_(x rarr 0^(+)) f(x) = 3, lim_(x rarr 0^(-)) f(x) = 4 and f(0) = 5 , then the image of the point (0, 1) about the line, y.lim_(x rarr 0) f(cos^(3) x - cos^(2) x) = x. lim_(x rarr 0) f(sin^(2) x - sin^(3) x) , is a. ((12)/(25),(-9)/(25)) b. ((12)/(25),(9)/(25)) c. ((16)/(25),(-8)/(25)) d. ((24)/(25),(-7)/(25))

If f(x) is continuous at x=0 , where f(x)=sin x-cos x , for x!=0 , then f(0)=

Let f (x) =(ax+b)/(x+1), lim_(x rarr 0)f(x)=2 and lim_(x to oo)f(x)=1 , Prove that f (- 2) = 0.

If f'(x)=3x^(2)sin x-x cos x ,x!=0 f(0)=0 then the value of f((1)/(pi)) is

If g(x) = (x^(2)+2x+3) f(x) and f(0) = 5 and lim_(x rarr 0) (f(x)-5)/(x) = 4, then g'(0) =