009A Sample Final 2, Problem 9

Compute

a) $\lim _{x\rightarrow 4}{\frac {{\sqrt {x+5}}-3}{x-4}}$

b) $\lim _{x\rightarrow 0}{\frac {\sin ^{2}x}{3x}}$

c) Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \lim_{x\rightarrow -\infty} \frac{\sqrt{x^2+2}}{2x-1}}

Foundations:

Solution:

(a)

Step 1:

Step 2:

(b)

Step 1:

Step 2:

(c)

Step 1:

Step 2:

Final Answer:
(a)
(b)
(c)

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