On what interval is the function \(f(x)=-x^3+2x^2+5\) increasing and concave downward?

Solution.

On what interval is the function \(f(x)=-x^3+4x^2-5x\) decreasing and concave downward?

Solution.

Find the limit \(\lim_{x\to0^+}(\sin x)^{\sin x}\).

Solution.

Find the limit \(\lim_{x\to0^+}(\sin x)^{\tan x}\).

Solution.

Find the limit \(\lim_{x\to0^+}(\tan x)^{\sin x}\).

Solution.

Find the limit \(\lim_{x\to0^+}(\tan x)^{\tan x}\).

Solution.