Calculus I - Limits At Infinity, Part I (Practice Problems)

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Section 2.7 : Limits at Infinity, Part I

For f(x)=4x7−18x3+9 evaluate each of the following limits.
1. $\mathop {\lim }\limits_{x \to \, - \infty } f\left( x \right)$
2. $\mathop {\lim }\limits_{x \to \,\infty } f\left( x \right)$
Solution
For h(t)=3√t+12t−2t2 evaluate each of the following limits.
1. $\mathop {\lim }\limits_{t \to \, - \infty } h\left( t \right)$
2. $\mathop {\lim }\limits_{t \to \,\infty } h\left( t \right)$
Solution

For problems 3 – 10 answer each of the following questions.

(a) Evaluate $\mathop {\lim }\limits_{x \to \, - \infty } f\left( x \right)$

(b) Evaluate $\mathop {\lim }\limits_{x \to \,\infty } f\left( x \right)$

(c) Write down the equation(s) of any horizontal asymptotes for the function.

$\displaystyle f\left( x \right) = \frac{{8 - 4{x^2}}}{{9{x^2} + 5x}}$ Solution
$\displaystyle f\left( x \right) = \frac{{3{x^7} - 4{x^2} + 1}}{{5 - 10{x^2}}}$ Solution
$\displaystyle f\left( x \right) = \frac{{20{x^4} - 7{x^3}}}{{2x + 9{x^2} + 5{x^4}}}$ Solution
$\displaystyle f\left( x \right) = \frac{{{x^3} - 2x + 11}}{{3 - 6{x^5}}}$ Solution
$\displaystyle f\left( x \right) = \frac{{{x^6} - {x^4} + {x^2} - 1}}{{7{x^6} + 4{x^3} + 10}}$ Solution
$\displaystyle f\left( x \right) = \frac{{\sqrt {7 + 9{x^2}} }}{{1 - 2x}}$ Solution
$\displaystyle f\left( x \right) = \frac{{x + 8}}{{\sqrt {2{x^2} + 3} }}$ Solution
$\displaystyle f\left( x \right) = \frac{{8 + x - 4{x^2}}}{{\sqrt {6 + {x^2} + 7{x^4}} }}$ Solution