Math

h.w17.docx

In each problem for which you decide to use L' Hopital's Rule and when you convert your expression to a fraction, check and state that the hypotheses of the theorem are satifsied. Before submitting your homework, check all problems by graphing the function near the limit and see if the values support your solution.

Find limits. Use L'Hospital's Rule when appropriate. If there is a more elementary algebraic method, you might consider it.

1. imit as (x to 0) [sin x]/[3 x] .

2. imit as (x to 0) [cos x]/[sin x+1] .

3. imit as (x to infinity) x e^(-x) .

4. imit as (x to-infinity) (x^2-x^4) .

5. imit as (x to 1) [x^5-1]/[x-1] .

6. imit as (t to 0) [3^t-2^t]/t .

7. imit as (x to 1) [ln x]/[sin (pi x)] .

8. imit as (x to 0+) x^(2 x) .

9. imit as (x to infinity) (root (x^2-20 x+3)-x) (Is LH really needed here? What value does a graph suggest?).

10. The graphs of (x) and (x) are shown below. Estimate imit as (x to 0) [f(x)+2]/[g(x)-3] by using L'Hospital's Rule. Explain why you can apply this rule.

ttp://calculus.sfsu.edu/latexrender/pictures/6c52da9ef91e0ab764e5a1c4c66003fd.png

11. Based on the graph below estimate imit as (h to 2) [f(h)]/[g(h)] . Explain in a sentence how you are estimating this limit.