(6) Use the series representation of the function to approximate the integral with € < 10-4.Hint: Upon integrating the series use Alternating Series Remainder formula.(c)(a) [e-² dadxsin x(b) √'sXdxcos(cos(√x) dx

(6). (a) Given the integral is ∫01e-x2dx.

Answered: (6) Use the series representation of…

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter8: Further Techniques And Applications Of Integration

Section8.4: Improper Integrals

Problem 13E

See similar textbooks

Similar questions

Solve for x: z=x.
Use the difference to find a power series representation for the function f(x)=3/(1+x)2.
B 25- A) Use series to express the function f(x) = coshx. the
2. Use differentiation to find a power series representation for f(x) = 1 (1 + x)²
cos (6x2 Let f(x) 1 Evaluate the 10th derivative of f at x = 0. x2 f(10) (0) = Hint: Build a Maclaurin series for f(x) from the series for cos(æ).
Q4. Find the Fourier sine series for the function: f(x)= 0 for for 0
The function f(x)=3xln(1+x) is represented as a power series
32 (a) Evaluate the integral: dx x2 + 4 Your answer should be in the form k, where k is an integer. What is the value of k? d 1 -arctan(x) dx Hint: x2 + 1 k = (b) Now, let's evaluate the same integral using a power series. First, find the power series for the function 32 .. Then, integrate it from 0 to 2, and call the result S. S should be an infinite series. x2 + 4 f(x) What are the first few terms of S? an = aj = az = az = a4 = (c) The answers to part (a) and (b) are equal (why?). Hence, if you divide your infinite series from (b) by k (the answer to (a)), you have found an estimate for the value of T in terms of an infinite series. Approximate the value of T by the first 5 terms. (d) What is the upper bound for your error of your estimate if you use the first 8 terms? (Use the alternating series estimation.)

Recommended textbooks for you

Calculus For The Life Sciences

Calculus

ISBN:

9780321964038

Author:

GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:

Pearson Addison Wesley,

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:

9781133382119

Author:

Swokowski

Publisher:

Cengage

College Algebra (MindTap Course List)

Algebra

ISBN:

9781305652231

Author:

R. David Gustafson, Jeff Hughes

Publisher:

Cengage Learning

Calculus For The Life Sciences

Calculus

ISBN:

9780321964038

Author:

GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:

Pearson Addison Wesley,

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:

9781133382119

Author:

Swokowski

Publisher:

Cengage

College Algebra (MindTap Course List)

Algebra

ISBN:

9781305652231

Author:

R. David Gustafson, Jeff Hughes

Publisher:

Cengage Learning

SEE MORE TEXTBOOKS

(6) Use the series representation of the function to approximate the integral with € < 10-4. Hint: Upon integrating the series use Alternating Series Remainder formula. (2) ²¹-2² dr. (h) (¹sin.x (cos(√T) dr dr (c)