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Practice Problems for 2/13

  1. Explain what an indeterminate form is and why we have use algebraic manipulation when calculating such limits.

  2. Calculate the following limits or show they do not exist. Be sure to show all necessary steps.
    1. \(\lim_{x\rightarrow \infty} \frac{15x^7+6x^2+11}{5x^7+x}\)

    2. \(\lim_{x\rightarrow \infty} \frac{x^{7/2}+11x^{2/3}+3}{4x^4+2x^2+1}\)

  3. Calculate the following limits or show they do not exist. Be sure to show all necessary steps.
    1. \(\lim_{x\rightarrow \infty} \sqrt{7x^6+9}-x^3\)
    2. \(\lim_{x\rightarrow \infty} \sqrt{x^2+x}-\sqrt{x^3+x}\)