Given two curves: `y=f(x)` passing through the point `(0,1)` and `g(x)=int_(-oo)^xf(t)dt` passing through the point `(0,1/n)dot` The tangents drawn to both the curves at the points with equal abscissas intersect on the x-axis. Find the curve `y=f(x)dot`

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 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

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

Find the equations of the tangent and the normal to the curve y = x^2 + 4x + 1 at the point whose abscissa is 3.

The circle passing through the point ( -1,0) and touching the y-axis at (0,2) also passes through the point.

Find the equations of the tangent and normal to the given curves at the points given y = x^2 at (0,0)

The equation of the tangents to the curve (1+x^(2))y=1 at the points of its intersection with the curve (x+1)y=1 , is given by

Show that x/a+y/b=1 touches the curve y=be^(-x//a) at the point, where the curve crosses the y-axis.

Find the equation of a curve passing through the origin if the slope of the tangent to the curve at any point (x,y) is equal to the square of the difference of the abscissa and the ordinate of the point.