Linear Piece Matched to a Power Function

Difficulty: Hard · Topics: Calculus, Derivatives, Continuity

Darajali funksiyaga ulangan chiziqli bo‘lak

Let g(x) be a linear function and

f(x)=begincases g(x), & x≤ 0 \\[6pt] ≤ft((1+x)/(2+x) )^1/x, & x 0 endcases

is continuous at x=0. If f'(1)=f'(-1), then calculate g(3).