Calculus 1

$\lim_{x\rightarrow 0} \frac{\tan{x}}{x}$

$\lim_{x\rightarrow 0} \frac{\sin{(3x)}}{x}$

Compute $f'(x)$ using the limit definition of the derivative $f'(a) = \lim_{h \to 0} \frac{f(a+h) - f(a)}{h}$ for the following 1. f(x) = 3 2. f(x) = 3x-1 3. f(x) = $x^2 + x$ 4. f(x) = $\sqrt(x)$ 5. f(x) = 1/x

Find the derivative of the following function using the limit definition of derivative,

$f(x) = 8x + 4$

Use the definition of derivatives to find the derivative of the following function,

$f(x) = \sqrt{x - 1}$

Find the slope of the tangent line to

$f(x) = \sqrt{x}$

when x = 1

Find the slope of the tangent line to

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

when x = 4

Use the definition of the derivative to find $f\prime(x)$ if

$f(x) = \frac{2}{3 - 5x}$

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.

Use the product rule to find the derivative of

$f(x) = (x^3 + 5x)(2x^2)$

Find the derivative of $f(x) = \sin{x}(x^2 + 5)$

Find the derivative of $y = 2x^2 + 3x - 17$

Find the derivative of $f(x) = x$

Find the derivative of $f(x) = \frac{1}{x^2}$

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

Find the derivative of the function,

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

Use the power rule to find the derivative of $f(x) = 2x^5$

Use the power rule to find the derivative of $f(x) = 2x^{\frac{3}{2}}$