- Please take the time to evaluate the questions before continuing on to the solutions.
- There are only a few questions up at this time. I plan on add on to this list in the coming days.
- If you have any questions please contact me.
- (scroll past the problems to get the answers)

**Problem #1:**Find the Limit of the function.

$\lim _{x\to {\frac {\pi }{4}}}{\frac {\tan(x)-1}{x-{\frac {\pi }{4}}}}$

**Problem #2:**Find the derivative of the tangent function using the quotient rule.

${\frac {d}{dx}}\tan(x)={\frac {\sin(x)}{\cos(x)}}$

**Problem #3:**Find the slope of the tangent line at point P(4,.5).

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

**Problem #4:**Find the limit.

- current problem (hint: think substitution and the limits of "e")

$\lim _{x\to 0}{\frac {\ln(1+2x)}{x}}$

**Problem #1:**This tests your knowledge of trig identities.

$\lim _{x\to {\frac {\pi }{4}}}{\frac {\tan(x)-\tan({\frac {\pi }{4}})}{x-{\frac {\pi }{4}}}}$

$\lim _{x\to {\frac {\pi }{4}}}{\frac {{\frac {\sin(x)}{\cos(x)}}-{\frac {\sin({\frac {\pi }{4}})}{\cos({\frac {\pi }{4}})}}}{x-{\frac {\pi }{4}}}}$

$\lim _{x\to {\frac {\pi }{4}}}{\frac {\sin(x-{\frac {\pi }{4}})}{(x-{\frac {\pi }{4}})\cos({\frac {\pi }{4}})\cos(x)}}={\frac {1}{({\frac {\sqrt {2}}{2}})({\frac {\sqrt {2}}{2}})}}=2$

**Problem #2:** This is very basic.

${\frac {d}{dx}}\tan(x)={\frac {\cos(x){\frac {d}{dx}}\sin(x)-\sin(x){\frac {d}{dx}}\cos(x)}{\cos ^{2}(x)}}$

${\frac {d}{dx}}\tan(x)={\frac {\cos ^{2}(x)+\sin ^{2}(x)}{\cos ^{2}(x)}}$

${\frac {d}{dx}}\tan(x)=\sec ^{2}(x)$

**Problem #3:**This is quite basic.

$f'(x)={\frac {{\sqrt {x}}-{\sqrt {x+h}}}{h{\sqrt {x}}{\sqrt {x+h}}}}$

$f'(x)={\frac {-1}{2{\sqrt {x^{3}}}}}$