If `f(x)=cos^2x+s e c^2x ,t h e n` `f(x)<1` (b) `f(x)=1` (c) `2ltf(x)<1` (d) `""""f(x)ge2`

If f(x)=|0x-a x-b x+a0x-c x+b x+c0|,t h e n f(x)=0 (b) f(b)=0 (c) f(0)=0 f(1)=0

(1) If f(x)=a^(x)*e^(x^(2))" then find "f'(x)

If f(x)="cos"((log)_e x),t h e nf(x)f(y)-1/2[f(x/y)+f(x y)] has value (a) -1 (b) 1/2 (c) -2 (d) none of these

Find the one-sided limits of the following functions as x to 0 (a) f(x)=(1)/(2-2^(1//x)) (b) f(x)=e^(1//x) . (c ) f(x)=(|sin x|)/(x)

Let f:[0,1]rarrR (the set of all real numbers) be a function. Suppose the function f is twice differentiable, f(0)=f(1)=0 and satisfies f\'\'(x)-2f\'(x)+f(x) ge e^x, x in [0,1] Which of the following is true for 0 lt x lt 1 ? (A) 0 lt f(x) lt oo (B) -1/2 lt f(x) lt 1/2 (C) -1/4 lt f(x) lt 1 (D) -oo lt f(x) lt 0

A function f: R->R satisfies sinxcosy(f(2x+2y)-f(2x-2y)=cosxsiny(f(2x+2y)+f(2x-2y))dot If f^(prime)(0)=1/2,t h e n (a)f^(prime)(x)=f(x)=0 (b)4f^(x)+f(x)=0 (c)f^(x)+f(x)=0 (d)4f^(x)-f(x)=0

If f(x)=(log)_(x^(2))(log x), then f'(x) at x=e is (a) 0(b)1(c)1/e (d) 1/2e

If f(x)=e^(x)(x^(2)+1) then find f'(x)

Off(x)=int_0^x("cos"(sint)+"cos"(cost)dt ,t h e nf(x+pi)i s (a)f(x)+f(pi) (b) f(x)+2(pi) (c)f(x)+f(pi/2) (d) f(x)+2f(pi/2)

If f(x)=log_(x^(2))(log x),quad then f'(x) at x=e is 0( b) 1 (c) (1)/(e) (d) (1)/(2)e