Question

1. Compute each of the following limits or show that it is $\infty$ or $-\infty$. (a) (2 points) $\lim_{x \to -3^{+}} \frac{|x+1| - 3}{x^2 + 2x - 3}$ (b) (2 points) $\lim_{x \to 0^{+}} \frac{2 \sin \frac{1}{x^2}}{\ln x}$ (c) (3 points) $\lim_{x \to 0} \frac{1 - 4^x}{1 - 8^x}$ (d) (3 points) $\lim_{x \to \pi} \frac{\cos x - \sec x}{\sin x}$ (e) (3 points) $\lim_{x \to -\infty} (2x + \sqrt{4x^2 + 3x})$

          1. Compute each of the following limits or show that it is $\infty$ or $-\infty$.
(a) (2 points) $\lim_{x \to -3^{+}} \frac{|x+1| - 3}{x^2 + 2x - 3}$
(b) (2 points) $\lim_{x \to 0^{+}} \frac{2 \sin \frac{1}{x^2}}{\ln x}$
(c) (3 points) $\lim_{x \to 0} \frac{1 - 4^x}{1 - 8^x}$
(d) (3 points) $\lim_{x \to \pi} \frac{\cos x - \sec x}{\sin x}$
(e) (3 points) $\lim_{x \to -\infty} (2x + \sqrt{4x^2 + 3x})$

1. Compute each of the following limits or show that it is ∞ or -∞.
(a) (2 points) limx → -3^+(|x+1| - 3)/(x^2 + 2x - 3)
(b) (2 points) limx → 0^+(2 sin(1)/(x^2))/(ln x)
(c) (3 points) limx → 0(1 - 4^x)/(1 - 8^x)
(d) (3 points) limx →π(cos x - sec x)/(sin x)
(e) (3 points) limx → -∞ (2x + √(4x^2 + 3x))

Added by Nathaniel W.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Piyush Kumar Gupta

03/07/2022

Step 1

So, |x+1| = -(x+1). lim -(x+1)-3 x→-3+ x^2 + 2x - 3 lim -x-4 x→-3+ x^2 + 2x - 3 lim -x-4 x→-3+ (x+3)(x-1) lim -x-4 x→-3+ (x-1) = -(-3)-4 / (-3-1) = -1 / -4 = 1/4 Show more…

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1. Compute each of the following limits or show that it is ∞ or -∞. (a) (2 points) lim |x+1|-3 x→-3+ x^2 + 2x - 3 (b) (2 points) lim 2 sin 1/x^2 x→0+ ln x (c) (3 points) lim 1-4^x x→0 1-8^x (d) (3 points) lim cos x - sec x x→π sin x (e) (3 points) lim (2x + √4x^2 + 3x) x→-∞