Problem 1

Find the vertical asymptotes, holes, and horizontal asymptotes of

$\huge \frac{x-5}{(x^2-16)(x^2 - 8x + 15)} $

and sketch a graph with all of them present

Problem 2

Find the following limits

$ \huge \lim_{x \to +/- \infty} \frac{9 x^5 - 3 x^2 + 3x}{x^2 + 2x + 10} $

Problem 3

Find the following limit

$ \huge \lim_{x \to +/-\infty} \frac{x^5 - 4x^2 + 1}{x^4 + 5x - 2x^5} $

Problem 4

Find the following limits

  • $\lim_{x \to \infty} x^{-5}$
  • $\lim_{x \to -\infty} 1$

Problem 5

Find the following limit

$ \huge \lim_{x \to +/- \infty} \frac{\cos(4x + 10)}{x^3} $

Problem 6

Find the horizontal asymptotes of the following function

$\Large f(x) = \frac{x^7}{2x^7 + \sqrt{x^{14} - x^{10} + 5 x^5}} $

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