Prove that the curves `y=f(x),[f(x)>0],a n dy=f(x)sinx ,w h e r ef(x)` is differentiable function, have common tangents at common points.

Prove that the function f given by f(x) = | x - 1|, x in R is not differentiable at x = 1

A function f satisfies the condition f(x)=f^(prime)(x)+f''(x)+f'''(x)....+infinity ,w h e r ef(x) is a differentiable function indefinitely and dash denotes the order of derivative. If f(0)=1,t h e nf(x) is e^(x/2) (b) e^x (c) e^(2x) (d) e^(4x)

Let g(x)=f(x)sinx ,w h e r ef(x) is a twice differentiable function on (-oo,oo) such that f'(-pi)=1. The value of |g^(-pi)| equals __________

Let g(x)=f(x)sinx ,w h e r ef(x) is a twice differentiable function on (-oo,oo) such that f'(-pi)=1. The value of g''(-pi) equals __________

Let g(x)=f(x)sinx ,w h e r ef(x) is a twice differentiable function on (-oo,oo) such that f(-pi)=1. The value of |g^''(-pi)| equals __________

If f(x)=x^n w h e r en in R , then differentiation of x^n with respect to xsin x^(n-1)dot

Prove that the function If f(x)={:{((x)/(1+e^(1//x)) ", " x ne 0),(" "0", " x=0):} is not differentiable

We are given the curves y=int_(-oo)^(x)f(t) dt through the point (0,(1)/(2)) and y=f(X), where f(x)gt0 and f(x) is differentiable, AAx in R through (0,1). If tangents drawn to both the curves at the point wiht equal abscissae intersect on the point on the X-axis, then int_(x to oo)(f(x))^f(-x) is

Prove that f(x)gi v e nb yf(x+y)=f(x)+f(y)AAx in R is an odd function.

Prove that f(x)gi v e nb yf(x+y)=f(x)+f(y)AAx in R is an odd function.