Partially Derivative: Sample Problems: Limits

18 March 2011

Sample Problems: Limits

I promised a post of me working out examples of solving limits, and here you go! 10 limit problems to give you an idea of how to solve this shit when you run across it. Click the problem for the solution. I tried to explain my process because I fucking hate it when books just do shit and leave you going "BUT WHERE DID THAT COME FROM??"

If you can't figure out wtf I was doing in any of these examples, leave a comment and I'll try to clarify.

Also, there's no L'Hospital ones in here. I didn't want to clutter up a limits post talking about derivatives. I'll do some L'Hospital examples in a later post, after I explain derivatives.

Definite limits:

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

2. $\lim_{x\to-4}\frac{x^2+5x+4}{x^2+3x-4}$

3. $\lim_{x\to2}\frac{x^2-x+6}{x-2}$

4. $\lim_{x\to-1}\frac{x^2-4x}{x^2-3x-4}$

5. $\lim_{x\to0^-}\left(\frac{1}{x}-\frac{1}{\left|x\right|} \right )$

Limits at infinity:

1. $\lim_{x\to\infty}\frac{1}{2x+3}$

2. $\lim_{x\to-\infty}\frac{1-x-x^2}{2x^2-7}$

3. $\lim_{y\to\infty}\frac{2-3y^2}{5y^2+4y}$

4. $\lim_{x\to-\infty}(x+\sqrt{x^2+2x})$

5. $\lim_{x\to-\infty}(x^4+x^5)$

Next time: Algebraic manipulation, probably. HUGE STEP BACK. All you non-calc folks can start reading again!

Partially Derivative

18 March 2011

Sample Problems: Limits

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