A Tangent, a Curve and the y-Axis
Difficulty: Hard · Topics: Calculus, Integration, Area
Urinma, egri chiziq va y o‘qi
The differentiable function f(x) has derivative
f'(x)=-x+e^1-x^2.
For a positive number t, let g(t) be the area enclosed by the tangent to y=f(x) at (t,f(t)), the curve y=f(x) and the y-axis. Find g(1)+g'(1).
Differensiallanuvchi f(x) funksiyaning hosilasi
f'(x)=-x+e^1-x^2.
Musbat t son uchun g(t) — y=f(x) ga (t,f(t)) nuqtada o‘tkazilgan urinma, y=f(x) egri chiziq va y o‘qi bilan chegaralangan yuza bo‘lsin. g(1)+g'(1) ni toping.