Question

1. lim_{x o 0} frac{sinx}{x} 2. lim_{x o 2} frac{x^2 - 5x + 6}{2x^2 - x - 7} 3. lim_{x o -3} frac{x^2 + 2x - 3}{2x^2 + 3x - 9} 4. lim_{x o 1} frac{7x + 8}{x^2 - 1} 5. lim_{x o infty} frac{e^{4x}}{ln(x)} 6. lim_{x o 0} frac{e^x - 1}{sinx}

          1. lim_{x 	o 0} frac{sinx}{x}
2. lim_{x 	o 2} frac{x^2 - 5x + 6}{2x^2 - x - 7}
3. lim_{x 	o -3} frac{x^2 + 2x - 3}{2x^2 + 3x - 9}
4. lim_{x 	o 1} frac{7x + 8}{x^2 - 1}
5. lim_{x 	o infty} frac{e^{4x}}{ln(x)}
6. lim_{x 	o 0} frac{e^x - 1}{sinx}

$1. limx o 0 fracsinxx 2. limx o 2 fracx^2 - 5x + 62x^2 - x - 7 3. limx o -3 fracx^2 + 2x - 32x^2 + 3x - 9 4. limx o 1 frac7x + 8x^2 - 1 5. limx o infty frace^4xln(x) 6. limx o 0 frace^x - 1sinx$

Added by Miriam S.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Madhur L

08/10/2023

Step 1

$\lim_{x \to 0} \frac{\sin x}{x}$ Using L'Hopital's rule, we differentiate the numerator and denominator with respect to x: $\lim_{x \to 0} \frac{\cos x}{1} = \cos 0 = \boxed{1}$ Show more…

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lim sin(x) / x as x approaches 0 lim (x^2 - 5x + 6) / (2x^2 - x - 7) as x approaches 2 lim (x^2 + 2x - 3) / (2x^2 + 3x - 9) as x approaches -3 lim (7x + 8) / (x^2 - 1) as x approaches 1 lim e^(4x) / ln(x) as x approaches infinity lim (e^x - 1) / sinx as x approaches 0