Curves `y=f(x)` passing through the point `(0,1)` and `y=int_-oo^x f(t) dt` passing through the point `(0,1/3)` are such that the tangents drawn to them at the point with equal abscissae intersect on x-axis. Answer the question:`lim_(xrarr0) ((f(x))^2-1)/x=` (A) `3` (B) `6` (C) `4` (D) none of these

Curves y=f(x) passing through the point (0,1) and y=int_-oo^x f(t) dt passing through the point (0,1/3) are such that the tangents drawn to them at the point with equal abscissae intersect on x-axis. Answer the question:The equation of curve y=f(x) is (A) y=e^(3x) (B) y=e^(x/3) (C) y=3^x (D) y=1/3^x

Curves y=f(x) passing through the point (0,1) and y=int_-oo^x f(t) dt passing through the point (0,1/3) are such that the tangents drawn to them at the point with equal abscissae intersect on x-axis. Answer the question:The area bounded by the curve y=f(x), y=x and ordinates x=0 and x=1 is (A) (e^2-1)/2 (B) (e^2-1)/3 (C) (e^3-1)/3 (D) none of these

Given the curves y=f(x) passing through the point (0,1) and y=int_(-oo)^(x) f(t) passing through the point (0,(1)/(2)) The tangents drawn to both the curves at the points with equal abscissae intersect on the x-axis. Then the curve y=f(x), is

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

The tangent to the curve y=x^(2)+3x will pass through the point (0,-9) if it is drawn at the point

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

If f'(x)=x-1, the equation of a curve y=f(x) passing through the point (1,0) is given by

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