
- Evaluate each of the following limits. Assume a is a positive constant. DO NOT USE...
(4) Use MacLaurin series to evaluate the following limits. Do not use L'Hospital's rule. (a) lim-0 21+ucos g -3 sin e 136.23-1 (b) lim 0 sin(6x)(e-1-1)
Use MacLaurin series to evaluate the following limits. Do not use L'Hospital's rule. (a) lim, 0 2x+cos 2-3 sino 1+36x3-1 (b) lim;-+0 sin(60)(et-1-2)
Indeterminate limits are often difficult. Sometimes simplifying the expression allows us to evaluate the limit, but many times there isn't a good way of simplifying. L'Hospital's rule is used to more easily evaluate these indeterminate limits. While this rule doesn't always work or apply, it generally makes a limit easier to evaluate when it does apply. 1. List as many types of indeterminate limits as you can. 2. State l'Hospital's rule in your own words. (There are actually several versions...
3. (5 points each) Evaluate the following limits or state that they do not exist ("DNE"). Use or -- if either is appropriate. Numbers alone without justification (either algebra and/or quoting theorems where applicable) will receive no credit. If you use L'Hôpital's Rule, clearly indicate when you do so. +3 (a) lim (b) lim 1.-1 cot(0) (c) lim
6. (10 pts) Let a be a positive integer Evaluate the following limit. If you use L'Hospital's Rule, be sure to give indeterminate type and mention when you invoke it. a' lim1+ t-00 04 7. (10 pts) The widths (in meters) of a kidney shaped swimming pool were measured at 2 meter intervals as indicated in the figure below. Use Simpson's Rule to estimate the area of the pool. Round answer to two decimal places. 5.0 72
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For numbers 5-7, use l'Hospital's rule to evaluate the following limits. 6. lim rins
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Evaluate the following limits using appropriate methods. Be sure to indicate each time L'Hôpital's Rule is used and the indeterminate form sin(1 - 32) 1. lim 2-1 -1
6. Use l'Hopital's rule to evaluate the following limits 1+cos (Te sin(z) (a) lim z-+0 log (-1) (b) lim 92I-2 cos(TI) (c) lim r sin Page 2 of 2 0 words
Evaluate the following limits. If you use L'Hopital's Rule, indicate on your paper that you have done so. If a limit is oo or - 0, then write oo or -oo. You may write DNE for does not exist. x² – 1 a.) lim Preview 7+1 In 4.q7 = - b.) lim 1+ I-4 2 – 3. - 4 Preview et -1 c.) lim 1+0 - sin(4x) Preview d.) limsin 4x = Preview Preview
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Find the limits and show your work. Use L'Hospital's Rule where appropriate. (a) lim-0 tan 3.0 2.2 1 (b) limu+0+ In(X) (c) limx→ In(x + 3) – In(3x + 2) (d) limz+ x sin(5) (e) lim.+ 22-45 4" +3: (f) limo (#2) (g) lim + (e+ + a)*