More practice problems.

1. Compute: $$\cfrac{1}{1+\cfrac{1}{1+1}}$$
2. Compute: $$\frac{1}{2}+ \cfrac{1}{1+\cfrac{1}{1+2}}$$
3. Simplify $$ (25 x^2) ^{3/2} $$
4. Differentiate $$ (25 x) ^{1/2} $$
a) once b) twice

Compute the following limits
5. $$\lim_{x \to \infty } \frac{x+2}{-3x + 4}$$
6. $$\lim_{x \to \infty } \frac{x^2+2x + 1}{3x^2 -4}$$
6. $$\lim_{x \to \infty } \frac{x+2}{x^2 + 4}$$
8. $$\lim_{x \to \infty } \frac{x^2 +2}{(1/3) x + 4}$$
9. $$\lim_{n \to \infty } \frac{n^3 + n^2 + n + 1}{n^2 + n + 1 }$$
10 . Find the value of the constant a so that $$\lim_{x \to \infty } \frac{(x+1)^2}{(a x -(1/a))^2} = 2/3$$
Compute the following limits
11. $$\lim_{x \to \infty } \frac{e^x+e^{-x}}{e^x - e^{-x}}$$
12. $$\lim_{x \to \infty } \frac{e^x}{100 x^{100}}$$
13. $$\lim_{x \to \infty } \frac{2 ^x }{e^x}$$
14. $$\lim_{x \to \infty } \frac{7 x^{15} }{e^{x/15}}$$ 15. $$ 1+\cfrac{1}{1+\cfrac{x}{1+ \cfrac{x}{1+\dots}}}$$ provided x is positive.{}