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Calculus Independent Study Path

Unit 4 Practice Test

Graph each of the following functions. Be sure to include critical points, inflection points, points of discontinuity, assymptotes, and limits at positive and negative infinity.

1.

y = \frac{x}{(x^{2} − 9)(x^{2} + 9)}

2.

y = \sqrt{\frac{x^{2} + 9}{x}}

Calculate the following limits:

3.

lim_{x→1} \frac{sin πx}{x − 1}

4.

lim_{x→0} \frac{cos(sin x) − 1}{x^{3}}