? - ? Forma. Estimate the value of by graphing over a
Chapter 4, Problem 81E(choose chapter or problem)
\(\infty-\infty\) Form
a. Estimate the value of
\(\lim _{x \rightarrow \infty}\left(x-\sqrt{x^{2}+x}\right)\)
by graphing \(f(x)=x-\sqrt{x^{2}+x}\) over a suitably large interval of \(x \text { - values }\).
b. Now confirm your estimate by finding the limit with l'Hôpital's Rule. As the first step, multiply \(f(x)\) by the fraction \(\left(x+\sqrt{x^{2}+x}\right) /\left(x+\sqrt{x^{2}+x}\right)\) and simplify the new numerator.
Equation Transcription:
values
Text Transcription:
infinity - infinity
lim over x rightarrow infinity (x - sqrt x^2+x)
f(x) = x - sqrt x^2 + x
x - values
f(x)
(x + sqrt x^2 + x)/(x + sqrt x^2 + x)
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