Question 4. Determine (if they exist) the following limits (using l'Hôpital's rule): In(1 + r) -...
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)
Question 2 (10 marks) In this question you must state if you use any standard limits, continuity, l'Hôpital's rule, the sandwich theorem or any convergence tests for series. You do not need to justify using limit laws 2n n3 or explain why it does not exist. (a) Evaluate lim n (b) Determine whether each of the following converge: n+3 2n (i) 2 (3n) (ii) (n3)! n=1 Question 2 (10 marks) In this question you must state if you use any...
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
Determine the exact value of the following limits using L'Hôpital's Rule where possible.
-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:
#2 1. (8 points) Evaluate the limit, without using L'Hôpital's Rule: x² – 2x - 3 lim 2+3 22 – 5x + 6 Note that 3 is a zero of the denominator polynomial, so you need to use the technique of Example 4.2.5(d) p. 113. 2. (8 points) In the previous problem, can L'Hôpital's Rule be applied? If so, evaluate the limit using L'Hôpital's Rule; if not, indicate how the limit expression does not satisfy the conditions required for L'Hôpital's...
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
do question 14 13. (-/6 Points] DETAILS LARCALC11 5.6.030. Evaluate the limit, using L'Hôpital's Rule if necessary. (If you need to use coor-co, enter INFINITY or --INFINITY, respectively.) lim x06 - X 14. [-15 Points] DETAILS LARCALC115.6.036.MI. Evaluate the limit, using L'Hôpital's Rule if necessary. In x2 lim * -
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)...
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...