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please show steps Evaluate the following limits using appropriate methods. Be sure to indicate each time...
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
-0. (incorrect) 8. (1 point) Compute the following limits using l'Hôpital's rule if appropriate. Use INF to denote oo and MINF to denote 1 - cos(8x) lim x+01 – cos(7x) 8x – 7* – 1 lim x² - 1 Answer(s) submitted: toy (incorrect) 9. (1 point) Compute the following limit using l’Hôpital's rule if appropriate. Use INF to denote oo and MINF to denote -0. lim 7 sin(x) ln(x) = x ot Answer(s) submitted:
Evaluate the following limits using l'Hôpital's Rule 10. lim sinx-2 x 7x3 10. lime sinti? 11. lim (1-3)* 12. lime e2-1 + 2x 12. lim 24-+2x 0
question c TOPIC 2: Trig Limits TRIG LIMITS: If direct substitution doesn't work, most triglimits can be solved by expressing the limit as a product of these special trig limits. 1. so also Lim 1 0 sinx |-cosx cos X-1 Lim - 0, so Lim =0, BUT Lim so useless! 01-Cos 0 Limsin 0 SQUEEZE THEOREM is covered and used for some proofs in the teaching videos, but will not be tested Q.14 Please evaluate the following limits, without using...
Evaluate the following limit. Use l'Hôpital's Rule when it is convenient and applicable. 2x4 + 5x + 4x +7 lim X + 1 Use l'Hôpital's Rule to rewrite the given limit so that it is not an indeterminate form. 2x + 5x +4% +7 lim lim X + 1 Evaluate the limit. lim 2x + 5x + 4x + 7 X+ 1 -(Type an exact answer.)
Evaluate the following limit using l'Hôpital's Rule. 7In x-7 lim X-e Xe Use l'Hôpital's Rule to rewrite the given limit so that it is not an indeterminate form. 7in x-7 lim X-e = lim Xe Xe Evaluate the limit. 7In x-7 7 = (Type an integer or a fraction.) lim X-e X-e n. Find the solution of the following initial value problem. p' (t) = 65 e -; (O) = 280 The solution of the initial value problem is p(t)...
4. Find the following limits by using L'Hôpital's rule. 1 + a) lim.-o 3 x cosx-sinx b) lim-o x sinx lim x-1x-1. c) 4. Find the following limits by using L'Hôpital's rule. 1 + a) lim.-o 3 x cosx-sinx b) lim-o x sinx lim x-1x-1. c)
2. [4 marks each] Evaluate each of the following limits, if possible. Provide an appropriate analytic argument to determine the value or to show that the limit does not exist. (a) lim +3x+2 x2-x-2 X-1
Question 4. Determine (if they exist) the following limits (using l'Hôpital's rule): In(1 + r) - 3 (a) lim (6) (1+r)-1 lim 22 (PER). 10 10 Verify that the assumptions of the theorem on l'Hôpital's rule are satisfied.
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...