Question

Math 180 Worksheets 5. (a) Evaluate the following limits. W2 i. \( \begin{aligned} \lim _{x \rightarrow-\infty} & {\left[-2 x^{4}-x^{2}-8 x\right] } \\ - & x\left(2 x^{3}+x^{2}-8\right)\end{aligned} \) iii. \( \lim _{x \rightarrow-\infty}\left[\frac{-6 x^{7}-4 x^{2}+2}{x^{2}-3 x+5}\right] \) \( -6 x^{2 t} \) ii. \( \lim _{x \rightarrow \infty}\left[\frac{3 x^{5}-x^{3}+8 x}{-5 x^{5}-7}\right] \) iv. \( \lim _{x \rightarrow \infty}\left[\frac{2 x^{2}-3 x}{x^{4}-7}\right] \) \( x\left(3 x^{4}-x^{2}+8\right) \) \( -5 x^{5}-1 \) \[ \frac{1}{x(2 x-3)} \] (b) Which, if any, of the functions above (i, ii, iii, iv) have horizontal asymptotes? Explain why using limits. 13

          Math 180 Worksheets
5. (a) Evaluate the following limits.

W2
i. \( \begin{aligned} \lim _{x \rightarrow-\infty} & {\left[-2 x^{4}-x^{2}-8 x\right] } \\ - & x\left(2 x^{3}+x^{2}-8\right)\end{aligned} \)
iii. \( \lim _{x \rightarrow-\infty}\left[\frac{-6 x^{7}-4 x^{2}+2}{x^{2}-3 x+5}\right] \)
\( -6 x^{2 t} \)
ii. \( \lim _{x \rightarrow \infty}\left[\frac{3 x^{5}-x^{3}+8 x}{-5 x^{5}-7}\right] \)
iv. \( \lim _{x \rightarrow \infty}\left[\frac{2 x^{2}-3 x}{x^{4}-7}\right] \)
\( x\left(3 x^{4}-x^{2}+8\right) \)
\( -5 x^{5}-1 \)
\[
\frac{1}{x(2 x-3)}
\]
(b) Which, if any, of the functions above (i, ii, iii, iv) have horizontal asymptotes? Explain why using limits.

13

Math 180 Worksheets
5. (a) Evaluate the following limits.

W2
i. limx →-∞ [-2 x^4-x^2-8 x]
- x(2 x^3+x^2-8)
iii. limx →-∞[(-6 x^7-4 x^2+2)/(x^2-3 x+5)]
-6 x^2 t
ii. limx →∞[(3 x^5-x^3+8 x)/(-5 x^5-7)]
iv. limx →∞[(2 x^2-3 x)/(x^4-7)]
x(3 x^4-x^2+8)
-5 x^5-1

(1)/(x(2 x-3))

(b) Which, if any, of the functions above (i, ii, iii, iv) have horizontal asymptotes? Explain why using limits.

13

Added by John D.

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