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Calculus Independent Study Path Unit 1 Practice Test

Evaluate the following limits, or state that they do not exist:

1.

lim_{h→0} \frac{(x + h)^{2} − x^{2}}{h}

2.

lim_{t→0} \frac{sin t}{1 + cos t}

3.

lim_{x→−3} ^{3} \sqrt{\frac{x + 3}{x^{3} + 27}}

4.

lim_{x→1} \frac{3x^{2} + 5}{x − 1}

5.

lim_{y→1} \frac{|y^{2} − 1|^{1/2}}{(y^{2} + 1)^{2}}

Determine the points of discontinuity of the following functions: 6.

f(x) = \begin{matrix}√ & \overline{9 − x} \\ √ & \overline{x − 6} \end{matrix}

7.

g(x) = \frac{5}{x^{3} − x^{2}}