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Question 2 (10 marks) In this question you must state if you use any standard limits, continuity, l'Hôpital's r...
clear explanation . tks (thumb) In this question you must state if you sandwich theorem. You do not need to justify usi...
clear explanation . tks (thumb)
In this question you must state if you sandwich theorem. You do not need to justify using limit laws. use any standard limits, continuity, l'Hôpital's rule or the C (a) Find the following limits if they exist 2 5 3x13 (i) lim x-o0 213 +9-1' (cosech r (ii) lim т-0L 2 COS (b) Let a, bE R be two arbitrary constants and consider the function for 1 2 — sech (аx —1) f(ar) 1 for...
Question 4. Determine (if they exist) the following limits (using l'Hôpital's rule): In(1 + r) -...
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.
f(x, y) = y/(sqrt(z? + y2) + x) Evaluate the limits below, if they exist. If the limit does not exist, explain why it d...
f(x, y) = y/(sqrt(z? + y2) + x) Evaluate the limits below, if they exist. If the limit does not exist, explain why it does not exist Yon musi elearly staie if you ity, lopital's rle or the sandwch theorem in your working. You do not need to justify using limit laws. (i) lim f(x, y) (ii) im f(r, y (iv) zlin2-1.0 arctan ^Ca.v)l
f(x, y) = y/(sqrt(z? + y2) + x)
Evaluate the limits below, if they exist. If...
1. Consider the function -F5 sin(r) for r f(x) =2 for 1< 3 2-25 for 3...
1. Consider the function -F5 sin(r) for r f(x) =2 for 1< 3 2-25 for 3 x2 -9x + 20 Evaluate the following limits You do not have to cite limit laws, but you must show how you arrived at your answer If a limit Does Not Exist, explain why. You should use oo or -oo where applicable Calculating the limit using L'Hopital's Rule will receive NO CREDIT. (a) lim f(x) r-+0 (b) lim f(x)= z-1 (e) lim f(z) (d)...
Question # 5. (8 marks) Determine which of the following series converge and which diverge (don't...
Question # 5. (8 marks) Determine which of the following series converge and which diverge (don't forget to state the tests from class that you are using!). If any of the convergent ones can be evaluated by the techniques we have learned in class, you should give their value as well. An: + 3n" + 7n +2 In(In(n)) (1) V3n13 - 2n° +55 +n +3 An In(n) 8] (ii) ns16 Σ (3n)! (n!) 33" (iv)
question c TOPIC 2: Trig Limits TRIG LIMITS: If direct substitution doesn't work, most triglimits can...
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...
Question # 5. (8 marks) Determine which of the following series converge and which diverge (don't...
Question # 5. (8 marks) Determine which of the following series converge and which diverge (don't forget to state the tests from class that you are using!). If any of the convergent ones can be evaluated by the techniques we have learned in class, you should give their value as well. 4 + 3n" + 7n +2 In(In(n)) (1) Σ 3n13 - 2n° +58 +n +3 4n In(n) (ii) 16
3. Use algebra, limit laws and/or Standard Limits for sequences to evaluate the following expression. You...
3. Use algebra, limit laws and/or Standard Limits for sequences to evaluate the following expression. You do not have to state explicitly which limit law(s) you are using. n! 4" n. n5n lim
b) first 6 (nl) 33" Question # 6. (6 marks) (a) Use the limit comparison test...
b) first
6 (nl) 33" Question # 6. (6 marks) (a) Use the limit comparison test to determine the convergence of the following: 2n + 5 m32n2 n2+1 3n+n +6 (11) n=1 2n + 5 n3+1 (iv) na + 2n² 3n7 +n +6 nel ni (b) Suppose I have polynomials f(x) and g(x) whose coefficients are all nonnegative. Determine when converges and wherrit dinerges. fin g(n) n=1 2
Question # 4. (5 marks) (a) State precisely our theorem on the convergence of telescoping series....
Question # 4. (5 marks) (a) State precisely our theorem on the convergence of telescoping series. (6) Evaluate the series, 2 2+ 6 35 2 21 + 6 4n2 + en + 3 +... 5 (c) Consider the statement: Suppose we have a sequence, {an} =1, and we can find another sequence, {Dm} 1 so that an = bn – Bn+2. If an converges then lim bn exists. n=1 Is this statement true? Either prove it (one may wish to...
clear explanation . tks (thumb)
In this question you must state if you sandwich theorem. You do not need to justify using limit laws. use any standard limits, continuity, l'Hôpital's rule or the C (a) Find the following limits if they exist 2 5 3x13 (i) lim x-o0 213 +9-1' (cosech r (ii) lim т-0L 2 COS (b) Let a, bE R be two arbitrary constants and consider the function for 1 2 — sech (аx —1) f(ar) 1 for...
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.
f(x, y) = y/(sqrt(z? + y2) + x) Evaluate the limits below, if they exist. If the limit does not exist, explain why it does not exist Yon musi elearly staie if you ity, lopital's rle or the sandwch theorem in your working. You do not need to justify using limit laws. (i) lim f(x, y) (ii) im f(r, y (iv) zlin2-1.0 arctan ^Ca.v)l
f(x, y) = y/(sqrt(z? + y2) + x)
Evaluate the limits below, if they exist. If...
1. Consider the function -F5 sin(r) for r f(x) =2 for 1< 3 2-25 for 3 x2 -9x + 20 Evaluate the following limits You do not have to cite limit laws, but you must show how you arrived at your answer If a limit Does Not Exist, explain why. You should use oo or -oo where applicable Calculating the limit using L'Hopital's Rule will receive NO CREDIT. (a) lim f(x) r-+0 (b) lim f(x)= z-1 (e) lim f(z) (d)...
Question # 5. (8 marks) Determine which of the following series converge and which diverge (don't forget to state the tests from class that you are using!). If any of the convergent ones can be evaluated by the techniques we have learned in class, you should give their value as well. An: + 3n" + 7n +2 In(In(n)) (1) V3n13 - 2n° +55 +n +3 An In(n) 8] (ii) ns16 Σ (3n)! (n!) 33" (iv)
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...
Question # 5. (8 marks) Determine which of the following series converge and which diverge (don't forget to state the tests from class that you are using!). If any of the convergent ones can be evaluated by the techniques we have learned in class, you should give their value as well. 4 + 3n" + 7n +2 In(In(n)) (1) Σ 3n13 - 2n° +58 +n +3 4n In(n) (ii) 16
3. Use algebra, limit laws and/or Standard Limits for sequences to evaluate the following expression. You do not have to state explicitly which limit law(s) you are using. n! 4" n. n5n lim
b) first
6 (nl) 33" Question # 6. (6 marks) (a) Use the limit comparison test to determine the convergence of the following: 2n + 5 m32n2 n2+1 3n+n +6 (11) n=1 2n + 5 n3+1 (iv) na + 2n² 3n7 +n +6 nel ni (b) Suppose I have polynomials f(x) and g(x) whose coefficients are all nonnegative. Determine when converges and wherrit dinerges. fin g(n) n=1 2
Question # 4. (5 marks) (a) State precisely our theorem on the convergence of telescoping series. (6) Evaluate the series, 2 2+ 6 35 2 21 + 6 4n2 + en + 3 +... 5 (c) Consider the statement: Suppose we have a sequence, {an} =1, and we can find another sequence, {Dm} 1 so that an = bn – Bn+2. If an converges then lim bn exists. n=1 Is this statement true? Either prove it (one may wish to...
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