Let `f: RvecR` be such that `f(a)=1,f^(prime)(a)=2.` Then `(lim)_(xvec0)((f^2(a+x))/(f(a)))^(1//x)` is a. `e^2` b. `e^4` c. `e^(-4)` d. `1//e`

Let f:R rarr R be such that f(1)=3andf'(1)=6. Then lim_(x rarr0)((f(1+x))/(f(1)))^(1/x)=(a)1( b) e^((1)/(2))(c)e^(2) (d) e^(3)

f(x)=e^x then lim_(x rarr 0) f(f(x))^(1/{f(x)} is

Let R rarr R be such that f(1)=3 and *f'(1)=6. then lim_(x rarr0)((f(1+x))/(f(1))) equal : (1)1(2)e^((1)/(2))(3)e^(2) (4) e^(3)

I=int_(0)^(2)(e^(f(x)))/(e^(f(x))+e^(f(2-x)))dx is equal to

Let a function f(x) be such that f"(x)=f'(x)+e^(x)&f(0)=0,f'(0)=1 then find the value of ln(((f(2))^(2))/(4))

f(x)=|cos xx1 2sinxx^2 2xtanxx1| . Then value of (lim)_(xvec0)(f(x))/x is equal to 1 b. -1 c. zero d. none of these

Suppose f is a differentiable real function such that f(x)+f^(prime)(x)lt=1 for all x , and f(0)=0, then the largest possible value of f(1) is (1) e^(-2) (2) e^(-1) (3) 1-e^(-1) (4) 1-e^(-2)

If 3x+2y=1 is a tangent to y=f(x) at x=1//2 , then lim_(xrarr0) (x(x-1))/(f((e^(2x))/(2))-f((e^(-2x))/(2)))

Let f(x) be a continuous function such that f(a-x)+f(x)=0 for all x in [0,a] . Then int_0^a dx/(1+e^(f(x)))= (A) a (B) a/2 (C) 1/2f(a) (D) none of these