8x 2x 32x 128x 3 +... 7.
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
Use the table in the picture to help you find a Function with the indicated series representation.
![Table 11.5
= 1 + x + x² +.. +x* + . ..
1 - x
Σ, for lx <1
%3D
=1- x + x² -
(-1)** + =
(-1)*x*, for |x| < 1
%3D
1 + x
et = 1 + x +
2!
for |x| < ∞
%3D
k!
k!'
(-1)*x2k+1
(2k + 1)!
(-1)*x2*+1
(2k + 1)! '
sin x = x -
3!
for |x < 0
1.
t
5!
k=0
.2k
(-1)*x*
(-1)* x²*
cos x = 1 -
2!
for x < ∞
4!
(2k)!
(2k)!
k=0
x²
In (1 + x) = x -
(-1)*+1 x*
(-1)*+1,k
for -1 < x S< 1
3
k=1
x²
-In (1 – x) = x +
.3
+ ·
k
for -1 < x < 1
k=1
(-1)*x2%+1
(-1)* x2*+1
8.
tanx = x -
3.
for |x s 1
2k + 1
2k + 1
k=0
2k
2k +1
sinh x = x +
3!
+...+
5!
for x < ∞
(2k+1)!
k=0(2k + 1)!"
x²
cosh x = 1 +
2!
2k
Σ
(2k)!"
for x < ∞
+.
%3D
4!
(2k)!
E. for lal < 1 and (P) - Pp - Dp - 2) (P – k + 1) (P) - 1
p(p 1)(p - 2)-- (p – k + 1)
(.)
(1 + x) =
, for x< 1 and
%3D
3D1
k!
8.
8.
8.
8.
8.
||
8.
||
8.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7a6e6fa2-624a-47a3-bf18-e2313eb69562%2Ffe8a00db-6751-4bf2-a574-ac82528ceed9%2Fijy9k1d.jpeg&w=3840&q=75)
Transcribed Image Text:Table 11.5
= 1 + x + x² +.. +x* + . ..
1 - x
Σ, for lx <1
%3D
=1- x + x² -
(-1)** + =
(-1)*x*, for |x| < 1
%3D
1 + x
et = 1 + x +
2!
for |x| < ∞
%3D
k!
k!'
(-1)*x2k+1
(2k + 1)!
(-1)*x2*+1
(2k + 1)! '
sin x = x -
3!
for |x < 0
1.
t
5!
k=0
.2k
(-1)*x*
(-1)* x²*
cos x = 1 -
2!
for x < ∞
4!
(2k)!
(2k)!
k=0
x²
In (1 + x) = x -
(-1)*+1 x*
(-1)*+1,k
for -1 < x S< 1
3
k=1
x²
-In (1 – x) = x +
.3
+ ·
k
for -1 < x < 1
k=1
(-1)*x2%+1
(-1)* x2*+1
8.
tanx = x -
3.
for |x s 1
2k + 1
2k + 1
k=0
2k
2k +1
sinh x = x +
3!
+...+
5!
for x < ∞
(2k+1)!
k=0(2k + 1)!"
x²
cosh x = 1 +
2!
2k
Σ
(2k)!"
for x < ∞
+.
%3D
4!
(2k)!
E. for lal < 1 and (P) - Pp - Dp - 2) (P – k + 1) (P) - 1
p(p 1)(p - 2)-- (p – k + 1)
(.)
(1 + x) =
, for x< 1 and
%3D
3D1
k!
8.
8.
8.
8.
8.
||
8.
||
8.
![8x
2x
32x 128x
+.
+...
3.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7a6e6fa2-624a-47a3-bf18-e2313eb69562%2Ffe8a00db-6751-4bf2-a574-ac82528ceed9%2Fh8t7aft.jpeg&w=3840&q=75)
Transcribed Image Text:8x
2x
32x 128x
+.
+...
3.
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