Differentiability of a Piecewise Function
Difficulty: Medium · Topics: Calculus, Derivatives, Continuity
Bo‘lakli funksiyaning differensiallanuvchanligi
The function f(x) is differentiable at x=1.
f(x)=begincases ae^-x, & x 1 \\[6pt] bsin≤ft((π)/(2)x )-x+1, & x≤ 1 endcases
Find a+b. (a, b are constants.)
f(x) funksiya x=1 nuqtada differensiallanuvchi.
f(x)=begincases ae^-x, & x 1 \\[6pt] bsin≤ft((π)/(2)x )-x+1, & x≤ 1 endcases
a+b ni toping. (a, b — o‘zgarmaslar.)