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13 Nov 2019
MATH 100 / MATH 109 UUsing Derivatives Using Derivatives... 1. ... to evaluate limits: (a) Explain why the limit lim +e* 100 et -e- is in a suitable form for applying l'Hospital's rule. (b) Attempt to evaluate lim ette will need to use l'Hospital's rule more than once to see the problem). 10 et -e- by applying l'Hospital's rule. What went wrong? (You (c) Without using l'Hospital's rule, show that lim +00 et -e-2 2. ... to optimize things: Of all the lines tangent to y = 12, find the equation of the one with the largest slope. 3. ... to approximate things: e* +e-* (a) Approximate ln(1.01) by using an appropriate linearization, and by using one iteration of Newton's method on an appropriate function. (b) Explain why we cannot use Newton's method to find a root of f(x) = 13 â 23 + 2 with initial guess 10 = 1. Illustrate your explanation with a sketch. Note: To see the problem you will need to do more than one iteration of Newton's method. 4. ... to prove things: (a) Prove that 25 + +1 has exactly one zero on [-2, 2). (b) Suppose that a runner completes a 3 mile race in 16 minutes. Assume that her initial speed is 0 and her speed at the end of the race is also 0. Prove that she was running at exactly 11 miles per hour at least two times during the race.
MATH 100 / MATH 109 UUsing Derivatives Using Derivatives... 1. ... to evaluate limits: (a) Explain why the limit lim +e* 100 et -e- is in a suitable form for applying l'Hospital's rule. (b) Attempt to evaluate lim ette will need to use l'Hospital's rule more than once to see the problem). 10 et -e- by applying l'Hospital's rule. What went wrong? (You (c) Without using l'Hospital's rule, show that lim +00 et -e-2 2. ... to optimize things: Of all the lines tangent to y = 12, find the equation of the one with the largest slope. 3. ... to approximate things: e* +e-* (a) Approximate ln(1.01) by using an appropriate linearization, and by using one iteration of Newton's method on an appropriate function. (b) Explain why we cannot use Newton's method to find a root of f(x) = 13 â 23 + 2 with initial guess 10 = 1. Illustrate your explanation with a sketch. Note: To see the problem you will need to do more than one iteration of Newton's method. 4. ... to prove things: (a) Prove that 25 + +1 has exactly one zero on [-2, 2). (b) Suppose that a runner completes a 3 mile race in 16 minutes. Assume that her initial speed is 0 and her speed at the end of the race is also 0. Prove that she was running at exactly 11 miles per hour at least two times during the race.
Nelly StrackeLv2
15 Aug 2019