(a). Compute the exact value of the integral f te-tdt . (b). Compute the integral ( sin? x cos x dx. ( Round-off your answer to the nearest five decimal places.)
(a). Compute the exact value of the integral f te-tdt . (b). Compute the integral ( sin? x cos x dx. ( Round-off your answer to the nearest five decimal places.)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Transcribed Image Text:09:35
81
(a). Compute the exact value of the
integral f te-tdt .
(b). Compute the integral
,3
| sin? x cos x dx. (Round-off your
2
answer to the nearest five decimal
places.)
(c). Draw and compute the area of the
region bounded by the lines
У1 — х +1, У2 — — 2х +7 and yз
-2x + 7 and
Y3
(c). Evaluate the improper integral
In dx
x2
1
(d). Let f E R be a differentiable
function of all order n E Z. Assume
that
![09:36
80
(d). Let f e R be a differentiable
function of all order n E Z. Assume
that
f(0) = 5, f'(0)
and f" (0) = 4
-3, f"(0) = 1
(i). Write down in terms of "x", a third
degree Taylor polynomial for f about
O and use it to approximate f(0.2).
P3(f)=
%3D
+
2
f(0.2) =
[Round-off to the nearest three decimal
places]
(ii). Write down a fourth degree
Maclaurine polynomial for t given that
t(x) = f(x²).
PA(4)(g(x)) = P2f(x²)
-3](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdd944e79-d6f4-433b-9501-ec696b91f7c4%2F4d733795-d3ba-42d0-96d9-b4b1c3bd380b%2Fgopc3rn_processed.png&w=3840&q=75)
Transcribed Image Text:09:36
80
(d). Let f e R be a differentiable
function of all order n E Z. Assume
that
f(0) = 5, f'(0)
and f" (0) = 4
-3, f"(0) = 1
(i). Write down in terms of "x", a third
degree Taylor polynomial for f about
O and use it to approximate f(0.2).
P3(f)=
%3D
+
2
f(0.2) =
[Round-off to the nearest three decimal
places]
(ii). Write down a fourth degree
Maclaurine polynomial for t given that
t(x) = f(x²).
PA(4)(g(x)) = P2f(x²)
-3
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