User talk:Srmeier

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[edit] Problems

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")

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

[edit] Answers

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

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

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

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