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3. (a) Why is L'Hospital's rule useful for finding the limits? Can it be used in every situation? Please justify your answer? (b) Evaluate each limit. Use L'Hospital's Rule where appropriate. i. lim x4-256 x→4 x-4 ii. lim x²-3x X-3 X-9

3. (a) Why is L'Hospital's rule useful for finding the limits? Can it be used in every situation? Please justify your answer? (b) Evaluate each limit. Use L'Hospital's Rule where appropriate. i. lim x4-256 x→4 x-4 ii. lim x²-3x X-3 X-9

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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3. (a) Why is L'Hospital's rule useful for finding the limits? Can it be used in every situation? Please justify your answer? (b) Evaluate each limit. Use L'Hospital's Rule where appropriate. i. lim x→4 x4. -256 ii. lim x-4 x²-3x x 3 x-9 (c)Finding an interest rate: Suppose you invest J$ 150,000 in a special 5 year savings account with a fixed annual rate r, with monthly compounding. The amount of money A in the account after 5years (60 months) is: A(r) = 150,000( 1 + r¹2). Your goal is to have $200,000 in the account after 5 years. i. Use the Intermediate value theorem to show there is a value of r in (0,0.07) that is an interest rate between 0% and 7% for which A(r) = 200,000. ii. Use a graphing utility to illustrate your explanation in part (i) and then estimate the interest rate required to reach your goal.
Transcribed Image Text:3. (a) Why is L'Hospital's rule useful for finding the limits? Can it be used in every situation? Please justify your answer? (b) Evaluate each limit. Use L'Hospital's Rule where appropriate. i. lim x→4 x4. -256 ii. lim x-4 x²-3x x 3 x-9 (c)Finding an interest rate: Suppose you invest J$ 150,000 in a special 5 year savings account with a fixed annual rate r, with monthly compounding. The amount of money A in the account after 5years (60 months) is: A(r) = 150,000( 1 + r¹2). Your goal is to have $200,000 in the account after 5 years. i. Use the Intermediate value theorem to show there is a value of r in (0,0.07) that is an interest rate between 0% and 7% for which A(r) = 200,000. ii. Use a graphing utility to illustrate your explanation in part (i) and then estimate the interest rate required to reach your goal.
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