009A Sample Midterm 1, Problem 1

Find the following limits:

a) Find $\lim _{x\rightarrow 2}g(x),$ provided that $\lim _{x\rightarrow 2}{\bigg [}{\frac {4-g(x)}{x}}{\bigg ]}=5$

b) Find $\lim _{x\rightarrow 0}{\frac {\sin(4x)}{5x}}$

c) Evaluate $\lim _{x\rightarrow -3^{+}}{\frac {x}{x^{2}-9}}$

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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