Evaluate each limit and justify your answer. 
lim x→2 (3 / 2x^5−4x^2−50)^4

Determine the end behavior of the following transcendental functions by analyzing appropriate limits. Then provide a simple sketch of the associated graph, showing asymptotes if they exist. 

$f\left(x\right)=\sin x$

Which one of the following intervals is not symmetric about x=5?

a.(1, 9)

b.(4, 6)

c.(3, 8)

d.(4.5, 5.5)

Find the following limits or state that they do not exist. Assume a, b , c, and k are fixed real numbers.

lim x→3 x − 3 /|x − 3|

Use the definitions given in Exercise 57 to prove the following infinite limits.

lim x→1^+ 1 /1 − x=−∞

Find all vertical asymptotes $x=a$ of the following functions. For each value of $a$, determine ${\(\displaystyle\)\(\lim\)_{x\(\to\) a^{+}}}f\(\left\)(x\(\right\))$, ${\(\displaystyle\)\(\lim\)_{x\(\to\) a^{-}}}f\(\left\)(x\(\right\))$, and ${\(\displaystyle\)\(\lim\)_{x\(\to\) a}}f\(\left\)(x\(\right\))$.

$f\left(x\right)=\frac{x+1}{x^3-4x^2+4x}$

Use the precise definition of infinite limits to prove the following limits.

$\underset{x\to 0}{\lim }(\frac{1}{x^4}-\sin \left(x\right))=\infty$