Prove that the curves `y_(1) = f (x) (f(x) gt 0)` and `y_(2) = f(x)` sin x, where f(x) is a differentiable function, are tangent to each other at the common points.

Prove that the curves y=f(x),[f(x)>0], and y=f(x)sin x, where f(x) is differentiable function,have common tangents at common points.

Solve: dy/dx=(y f\'(x)-y^2)/f(x) , where f(x) is a given function of x

f(x+y)=f(x).f(y)AA x,y in R and f(x) is a differentiable function and f'(0)=1,f(x)!=0 for any x.Findf(x)

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

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 The function f(x) is

We are given the curvers y=int_(- infty)^(x) f(t) dt through the point (0,(1)/(2)) any y=f(x) , where f(x) gt 0 and f(x) is differentiable , AA x in R through (0,1) Tangents drawn to both the curves at the points with equal abscissae intersect on the same point on the X- axists The function f(x) is

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 Number of solutions f(x) = 2ex is equal to

We are given the curvers y=int_(- infty)^(x) f(t) dt through the point (0,(1)/(2)) any y=f(x) , where f(x) gt 0 and f(x) is differentiable , AA x in R through (0,1) Tangents drawn to both the curves at the points with equal abscissae intersect on the same point on the X- axists The number of solutions f(x) =2ex is equal to

A function f satisfies the condition f(x)=f'(x)+f''(x)+f''(x)+…, where f(x) is a differentiable function indefinitely and dash denotes the order the derivative. If f(0) = 1, then f(x) is

If |f(x_1) - f(x_2)| le (x_1 - x_2)^(2), AA x_1 , x_2 in R . Find the equation of tangent to the curve y = f(x) at the point (1, 2) .