Let `f(x)={(sinx^2)/x x!=0
0x=0,` then `f^(prime)(0^+)+f^(prime)(0^-)` has the value equal to (a) 0 (b) 1 (c) 2 (d) None of these

If f(x)=int_0^1(dt)/(1+|x-t|) ,then f^(prime)(1/2) is equal to (a)0 (b) 1/2 (c) 1 (d) none of these

If f(x)=(x+1)^(cotx) be continuous at x=0, the f(0) is equal to (a) 0 (b) 1/e (c) e (d) none of these

Given the function f(x)=x^2e^-(2x) ,x>0. Then f(x) has the maximum value equal to a) e^-1 b) (2e)^-1 . c) e^-2 d) none of these

Let y=f(x) satisfies the equation f(x) = (e^(-x)+e^(x))cosx-2x+int_(0)^(x)(x-t)f^(')(t)dt The value of f(0)+f^(')(0) equal (a) -1 (b) 0 (c) 1 (d) none of these

If for a continuous function f,f(0)=f(1)=0,f^(prime)(1)=2 and y(x)=f(e^x)e^(f(x)) , then y^(prime)(0) is equal to a. 1 b. 2 c. 0 d. none of these

If for a continuous function f,f(0)=f(1)=0,f^(prime)(1)=2a n dy(x)=f(e^x)e^(f(x)) , then y^(prime)(0) is equal to a. 1 b. 2 c. 0 d. none of these

Let f(x)a n dg(x) be differentiable for 0lt=xlt=1, such that f(0)=0,g(0)=0,f(1)=6. Let there exists real number c in (0,1) such that f^(prime)(c)=2g^(prime)(c)dot Then the value of g(1) must be (a) 1 (b) 3 (c) -2 (d) -1

Let f(x)=(g(x))/x when x!=0 and f(0)=0. If g(0)=g^(prime)(0)=0 and g^ " (0)=17 then f^(prime)(0)= a). 3/4 b). -1/2 c). 17/3 d). 17/2

If f(x)a n dg(x) are differentiable functions for 0lt=xlt=1 such that f(0)=10 ,g(0)=2,f(1)=2,g(1)=4, then in the interval (0,1)dot (a) f^(prime)(x)=0 for a l lx (b) f^(prime)(x)+4g^(prime)(x)=0 for at least one x (c) f(x)=2g'(x) for at most one x (d) none of these

If f(x)a n dg(x) are differentiable functions for 0lt=xlt=1 such that f(0)=10 ,g(0)=2,f(1)=2,g(1)=4, then in the interval (0,1)dot (a) f^(prime)(x)=0 for a l lx (b) f^(prime)(x)+4g^(prime)(x)=0 for at least one x (c) f(x)=2g'(x) for at most one x (d) none of these