009A Sample Final 2, Problem 1

Compute

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

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

c) $\lim _{x\rightarrow -\infty }{\frac {\sqrt {x^{2}+2}}{2x-1}}$

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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