Limits, integrals

What are the two rules related with limits and natural log?

1. As $\lim_{n\to\infty}\ln\infty=\infty$

2. $$\lim_{n\to0^{+}}\ln\infty=-\infty$$

What is $\lim_{n\to\infty}r^{n}$ ? (Hint there is 2 answers)

1. If r < 1, then the limit approaches 0

2. If r > 1, then the limit approaches infinity

What is the limit rules for trigonometric functions

$$\lim_{x\to0}\frac{\sin x}{x}=0$$

What is the two rules for integrals over a symmetrical interval?

If the function is odd, then the integrals is 0

If the functoin is even, then

$$\int_{-a}^{a}f\left(x\right)=2\int_0^{a}f\left(x\right)$$

What are some even functions?

• Functions with even exponents

• Absolute value function

• Constant function

• cos(x), sec(x)