Question

求答案，微积分答案

Answer 1

2.f(x)=x²+4(a+1)x+2
f'(x)=2x+4(a+1)
令f'(x)≤0
2x+4(a+1)≤0
x≤-2(a+1)
因为递减区间为(-∞，-2]
所以
得-2(a+1)≥-2
得a+1≤1
a≤0
3.
lim (e^x - e^-x)/sinx
分子分母同乘e^x
=lim (e^2x -1)/(e^x sinx)
运用等价无穷小e^2x -1~2x，sinx~x
得
=lim 2x/(e^x *x)
=lim 2/e^x
=2/e^0
=2
4.
sin²5x求导
=2sin5x (sin5x)'
=2sin5x (5cos5x)
=10sin5xcos5x