009A Sample Midterm 2, Problem 1

Evaluate the following limits.

a) Find $\lim _{x\rightarrow 2}{\frac {{\sqrt {x^{2}+12}}-4}{x-2}}$

b) Find $\lim _{x\rightarrow 0}{\frac {\sin(3x)}{\sin(7x)}}$

c) Evaluate $\lim _{x\rightarrow ({\frac {\pi }{2}})^{-}}\tan(x)$

Foundations:
1. lim sinx/x
2. Left and right hand limit

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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