Calculus/Limits/Exercises

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For each limit, you should either compute it or work out why it doesn't exist. If it doesn't exist, what about the one-sided limits? Note that some of these may be \infty or -\infty.

[edit] Basic Limit Questions

(1) \quad\lim_{x\to 2} (4x^2 - 3x+1)

(2) \quad\lim_{x\to 5} (x^2)

[edit] Harder Limit Questions

(3) \quad\lim_{x\to 4} \frac{1}{x-4}

(4) \quad\lim_{x\to 2} \frac{1}{x-2}

(5) \quad\lim_{x\to -3} \frac{x^2 - 9}{x+3}

(6) \quad\lim_{x\to 3} \frac{x^2 - 9}{x-3}

(7) \quad\lim_{x\to -1} \frac{x^3+1}{x+1}

(8) \quad\lim_{x\to 4} \frac{x^2 + 5x-36}{x^2 - 16}

(9) \quad\lim_{x\to 25} \frac{x-25}{\sqrt{x}-5}

(10) \quad\lim_{x\to0} \frac{\left|x\right|}{x}

(11) \quad\lim_{x\to2} \frac{1}{(x-2)^2}

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