(b) Using the Taylor expansion of arctan x, 1

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
icon
Related questions
Question
Do the Part B in 10 minutes and Get the Thumbs up please show neat and clean work
Question 4
(a) Calculate the following:
i. the area of the region in the first quadrant bounded by the curves of
f(x)=√x and g(x)=x-2, and the x-axis. Show your working.
ii. the area of the region bounded by the curves of f(x) = sin and
g(x) = cosa in the interval [4, 5]. Show your workin
(b) Using the Taylor expansion of arctan x,
1<x< 1, calculate the sum
1
Σ(-1)", 3n (2n +1)
n=0
I
(c) Let f: [0, +∞o) → R be continuously differentiable. Show that there exist
continuous, positive and increasing functions g, h: [0, +∞) → R such
that f=g-h.
Hint: You may use the fact that for continuous functions g, h: [0, +∞) →
R, it holds that max{g, h}
g+h+g-hand min{g, h}
g+h-lg-hare
also continuous.
Transcribed Image Text:Question 4 (a) Calculate the following: i. the area of the region in the first quadrant bounded by the curves of f(x)=√x and g(x)=x-2, and the x-axis. Show your working. ii. the area of the region bounded by the curves of f(x) = sin and g(x) = cosa in the interval [4, 5]. Show your workin (b) Using the Taylor expansion of arctan x, 1<x< 1, calculate the sum 1 Σ(-1)", 3n (2n +1) n=0 I (c) Let f: [0, +∞o) → R be continuously differentiable. Show that there exist continuous, positive and increasing functions g, h: [0, +∞) → R such that f=g-h. Hint: You may use the fact that for continuous functions g, h: [0, +∞) → R, it holds that max{g, h} g+h+g-hand min{g, h} g+h-lg-hare also continuous.
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,