For the following exercise,

Use the Law of Cosines to solve for the missing angle of the oblique triangle. Round to the nearest tenth.

$a=14, b=13, c=20$; find angle $C$.

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Give the equations of any vertical, horizontal, or oblique asymptotes for the graph of each rational function. See the example in this section.

$$f(x)=\dfrac{4-3 x}{2 x+1}$$

Use a calculator to graph each rational function in the window indicated. Then (a) give the x- and y-intercepts, (b) explain why there are no vertical asymptotes, (c) give the equation of the oblique asymptote, and (d) give the domain and range.

$f(x)=\frac{x^3+4 x^2-x-4}{-2 x^2-2 x-4} ;[-4.7,4.7]$ by $[-3.1,3.1]$

Which function has a vertical asymptote at x=3 and an oblique asymptote?

a) f(x) = (x-3)/(x^2 - 9)

b) g(x) = (x^2 - 9)/(x-3)

c) h(x) = (x+3)/(x-3)

d) j(x) = (x^2 + 9)/(x-3)

Use a CAS to find the oblique asymptotes. Then use a graphing utility to draw the graph of $f$ and its asymptotes, and thereby confirm your findings. \

$$f(x)=\frac{3x^4 −4x^3 −2x^2 +2x +2}{x^3 −x}.$$

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Respond with true or false to given assertion. Be prepared to justify your answer.

The graph of $y=\frac{3 x^2+2 x+\sin x}{x}$ has an oblique asymptote of y=3 x+2.

Give the equations of any vertical, horizontal, or oblique asymptotes for the graph of each rational function. $f(x)=\frac{x-8}{2 x^{2}-9 x-18}$

Find the vertical, horizontal, and oblique asymptotes, if any, of each rational function. $F(x)=\frac{x^{2}+6 x+5}{2 x^{2}+7 x+5}$

Sketch a graph of the rational function and label the coordinates of the stationary points and inflection points. Show the horizontal, vertical, oblique, and curvilinear asymptotes and label them with their equations. Label point(s), if any, where the graph crosses an asymptote. Check your work with a graphing utility.

$$\frac { x ^ { 2 } - 2 } { x }$$

Determine whether the statement is true or false. Justify your answer. If any three sides or angles of an oblique triangle are known, then the triangle can be solved.

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Sketch a graph of the rational function and label the coordinates of the stationary points and inflection points. Show the horizontal, vertical, oblique, and curvilinear asymptotes and label them with their equations. Label point(s), if any, where the graph crosses an asymptote. Check your work with a graphing utility.

$$\frac { x ^ { 5 } } { x ^ { 2 } + 1 }$$