Calculus 1

$\lim_{x \rightarrow 4} \frac{x^2 - 16}{x - 4}$

$\lim_{x\rightarrow 9} \frac{\sqrt{x} - 3}{x - 9}$

$\lim_{x\rightarrow -3} \frac{x^2 - x + 12}{x + 3}$

$\lim_{x\rightarrow 0} \frac{\sqrt{2 - x} - \sqrt{2}}{x}$

$\lim_{ \theta\rightarrow 0} \frac{\cos(\theta) - 1}{\theta}$

Let $f(x) = \frac{3}{x - 5}$,

Evaluate the limit as $x\rightarrow 5^{-}$ and $x\rightarrow 5^{+}$

$\lim_{x\rightarrow \infty}\frac{3x^2 - 5x + 1}{x^3 - 1}$

$\lim_{x\rightarrow \infty} \frac{2x + 1}{\sqrt{x^2 - x}}$

Find the slope of the tangent line to

$f(x) = \frac{1}{x}$

when x = 4

Use the limit definition of the derivative to find the equation of the tangent line for the graph of

$y = x^2 - 3x + 2$ at (2, 0)

Use the limit definition of the derivative to find the equation of the normal line to the graph of

$f(x) = \frac{1}{\sqrt{4 - x}}$ at $x = 3$

Use the limit definition of the derivative to find all points on the graph of

$f(x) = 4x^3 - 12x^2 + 9x$

where the tangent lines to the graph have slope zero.

Find the Derivative of $f(x) = \sqrt[5]{x}$

Find the derivative of the function,

$y = 5x^3 - 4x - 1 + \frac{5}{x^4}$

What is the derivative of the following function

$f(x) = 15\sqrt[5]{x^2}$

Use the quotient rule to find the derivative of the following funciton,

$f(x) = \frac{x - 1}{x^2 + 2x + 1}$

Given $f(x)$, find the equation of the tangent line at the point $(-1, -2)$

$f(x) = \frac{4x}{(1 + x^2)}$

$g(x) = (x + 2 \sqrt x)e^x$

Show that the derivative of $\tan{x}$ is equal to $\sec^2{x}$

Use the quotient rule to find the derivative of $\csc{x}$