**Problem 10: Finding Indicated Limits**Find the indicated limits, if they exist (leave answers exact). Be sure to show all work!a. $\lim_{{x \to 6}} \frac{{-4x}}{{\sqrt{5x + 6}}}$b. $\lim_{{x \to -7}} \frac{{2x^2 + 15x + 7}}{{x + 7}}$c. $\lim_{{x \to 16}} \frac{{\sqrt{x} - 4}}{{x - 16}}$d. $\lim_{{x \to 4^+}} \frac{{x^2 + 2x - 4}}{{x - 4}}$

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Answered: 10. Find the indicated limits, if they…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

**Problem 10: Finding Indicated Limits**

Find the indicated limits, if they exist (leave answers exact). Be sure to show all work!

a. $\lim_{{x \to 6}} \frac{{-4x}}{{\sqrt{5x + 6}}}$

b. $\lim_{{x \to -7}} \frac{{2x^2 + 15x + 7}}{{x + 7}}$

c. $\lim_{{x \to 16}} \frac{{\sqrt{x} - 4}}{{x - 16}}$

d. $\lim_{{x \to 4^+}} \frac{{x^2 + 2x - 4}}{{x - 4}}$

Expert Solution

Step 1: Write the given limits

$Given space that space the space limits space a. limit as x rightwards arrow 6 of fraction numerator negative 4 x over denominator square root of 5 x plus 6 end root end fraction b. limit as x rightwards arrow negative 7 of fraction numerator 2 x squared plus 15 x plus 7 over denominator x plus 7 end fraction c. limit as x rightwards arrow 16 of fraction numerator square root of x minus 4 over denominator x minus 16 end fraction d. limit as x rightwards arrow 4 to the power of plus of fraction numerator x squared plus 2 x minus 4 over denominator x minus 4 end fraction$