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5. Evaluate the following limits: (a) $\lim_{x \to \infty} \frac{\ln x}{\sqrt{x}}$ (b) $\lim_{x \to 1} \frac{\ln x}{x - 1}$ 6. Use the guidelines of this section to sketch the curve: $y = x^4 - 8x$

          5. Evaluate the following limits:
(a) $\lim_{x \to \infty} \frac{\ln x}{\sqrt{x}}$
(b) $\lim_{x \to 1} \frac{\ln x}{x - 1}$
6. Use the guidelines of this section to sketch the curve: $y = x^4 - 8x$
        
5. Evaluate the following limits:
(a) limx →∞(ln x)/(√(x))
(b) limx → 1(ln x)/(x - 1)
6. Use the guidelines of this section to sketch the curve: y = x^4 - 8x

Added by Victoria J.

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Calculus: Early Transcendentals
Calculus: Early Transcendentals
James Stewart 8th Edition
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5. Evaluate the following limits: (a) lim Inr (b) lim In x x1x-1 6. Use the guidelines of this section to sketch the curve: y = x4 -- 8x 000 03
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Transcript

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00:01 Hi, in part a we have been given with limit x tends to pi 4 plus sin x minus 8x.
00:11 Evaluating this limit we get 4 plus sin of pi minus 8 into pi.
00:20 Now sin of pi is plus 1 so this is 4 into 1 minus 8 pi which is equal to 4 minus 8 pi and the answer is minus 21 .1324 that is approximately equal to minus 21 .13.
00:42 Question number b is limit x tends to 6 minus 3 minus x whole square upon x plus 6.
00:56 So this is equal to 3 minus x into 3 plus x upon x plus 6 and limit we will apply as x tends to 6 minus.
01:08 So this will be equal to 3 minus 6 into 3 plus 6 divided by 3 divided by 6 plus 6 that is equal to 3 minus 6 is 3 3 plus 6 is 9 divided by 12...
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