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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 largeinterval of $x$ -values.b. Now confirm your estimate by finding the limit withl'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 newnumerator.

a. $-\frac{1}{2}$b. $-\frac{1}{2}$

Calculus 1 / AB

Chapter 7

Transcendental Functions

Section 5

Indeterminate Forms and LHopitals Rule

Functions

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Lectures

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in this problem, we are given limit off function where we're gonna pull this election bikes. And we are first as the a graft function. You could use any. Oh, my function off. Porter, if you do that, you see that as extra. See infinity. So this is the XX. Is this functions now? The approaches to negative point. So then the limit from McGrath. You see, that movie was a big war house now. Important. This was part of a part feet we're gonna cut with this year's Eve. Look no true politicas except purchase it differently. And actually, we're given a hint we our asses to multiply both writer and intimidated by explosive period of expert. Plus you're right by X plus spirit of spirit. Plus thanks. The in the numerator people have limit is exposed to infinity. You don't have explained minus expiry place. Uh, X divided by now X in the Ninomiya is account from protector. So we can write this with this. Um thanks. One plus scrape bird one waas one over X. Now these will go away. X will cancel out, but on the limit will become limited's extra 50 50 um native one divided by one WAAS spirit of Warn plus four X as except purchase. See pretty this term we'll go to zeros and then this will be negative one over. Well, today's will be negative one, so it isn't safe.

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