User talk:Srmeier

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")

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

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

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

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

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

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.

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

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