Prove $f(x)$ is constant if $|f(x)-f(y)| < (x-y)^2$ for all real $x$ and $y$.

Find the limit $ \lim\limits_{x \to  0 } \frac{ \sin x – x \cos x}{ x^3 } $

Find the limit $ \lim\limits_{x \to  0 } \frac{ \tan x – x}{ x^3 } $

Will the following converge or diverge? $\sum\limits_{n=1}^\infty \frac{ (-1)^n x^n }{ \sqrt{1+n} } $

Will the following converge or diverge? $\sum\limits_{n=1}^\infty \frac{ 2^n x^n }{ n+1 } $  

Prove that p-series test from the integral test.

The functions $h(x)$ and $g(x)$ are differentiable such that the derivative of $h$ is $h$ and the derivative of $g$

Where (if anywhere) is the function $f(x)=x^3-3x^2+3x-1$ decreasing? Provide a sketch.

Prove  $e-1 \leq \int_{0}^{1} \left(1+x\right)^\frac{1}{2} e^x \leq \sqrt{2} \left(e-1\right) $

If the function $f$ is less than the function $g$ over some interval $a$ to $b$ and both functions are