[微積分一題]
版主: thepiano
Re: [微積分一題]
f(x) 在 x = 1 處連續
1^2 + 1 = (a * 1 + b)/(1 + 1)
a + b = 4
x ≦ 1，f'(x) = 2x
x ＞ 1，f'(x) = a/(x + 1) - (ax + b)/(x + 1)^2
f(x) 在 x = 1 處可微
2 = a/2 - (a + b)/4
a - b = 8
a = 6，b = -2
1^2 + 1 = (a * 1 + b)/(1 + 1)
a + b = 4
x ≦ 1，f'(x) = 2x
x ＞ 1，f'(x) = a/(x + 1) - (ax + b)/(x + 1)^2
f(x) 在 x = 1 處可微
2 = a/2 - (a + b)/4
a - b = 8
a = 6，b = -2