Suppose you wish to use a Taylor series for
(A) Explain why you would not use the Taylor series for f at 0.
(B) If you use the Taylor series for f at a, which value of a would you expect to yield the best approximation to the
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Calculus for Business, Economics, Life Sciences, and Social Sciences - Boston U.
- a. Use your calculator to approximate 0bex2dx for b=1,5,10and20. b. Based on your answer to part a, does 0ex2dx appear to be convergent or divergent? If convergent, what seems to be its approximate value? c. Explain why this integral should be convergent by comparing ex2withexforx1.arrow_forwarda. Use your calculator to approximate 0be0.00001xdx for b=10,50,100and1000. b. Based on your answer to part a, does 0e0.00001xdx appear to be convergent or divergent? c. To what value does the integral actually converge?arrow_forwardIf a coffee filter is dropped, its velocity after t seconds is given by v(t)=4(10.0003t) feet per second. What is the terminal velocity, and how long does it take the filter to reach 99 of terminal velocity? Use a table increment of 0.1 and given your answer to the nearest tenth of a second.arrow_forward
- -1 Estimate In(-x)dx by using a left-hand Riemann sum and 3 subintervals. -7 Complete the table of function values on page 4 and give the estimate as an exact value.arrow_forward2arctan(3r dr. 3. (а) Evaluate the indefinite integral 1+9z2 r16 (b) Suppose we know that "(3f(x) – 2) dr = 6 and that : rf(r?) dr = 8. Use this information and properties of integrals to find the value of f(z) dr.arrow_forward#2. Find the integralarrow_forward
- Evaluate the integral I = = √ (2x − 3x²/3) dr. 1. I = 2. I = −4 3. I = -5 16 3 4. I = −1 5. I = = 6. I = 6 5 5arrow_forwardSuppose we want to approximate the integral / r(x)dx by using a right-hand sum with 4 rectangles of equal widths. Write out this sum, using function notation for each term. Answer: 5 (r(1)+r(1.5) + r(2) + r(2.5)) Now, approximate the integral 3 | r(x)dx by using a left-hand sum with 3 rectangles of equal widths. Write out this sum, using function notation for each term. Answer: 2(r(4) +r(6) +r(8))arrow_forward5% Calculate the integral, assuming that f(x) dx = -2, f f(x) dx = 4, * f(x) dx = 10. (Use symbolic notation fractions where needed.) f(x) dx =arrow_forward
- f (2x² + 4x + 5) dz (a) Find the Riemann sum for this integral using right endpoints and n= = 3. R3 (b) Find the Riemann sum for this same integral, using left endpoints and n = = 3. Laarrow_forwardWe explore how Taylor polynomials can be used to calculate integrals which we otherwise do not know how to handle. Here we consider S V*. cos x dx, r1/4 replace cos x with the polynomial 1 - and give an estimate of the difference between • COs x dx and da = [,"" (»/ . ) 1/4 x2 r1/4 x5/2 So va. (1 *) dr = 1 1 221 2 0.082217269 - 2 2 12 7-27 2688 a) Write out Taylor's formula around 0 of degree three, f(x) = P3(x)+ E3(x), for f(x) = cos x.arrow_forward
- Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning