10:00 AM < Photo.pdf Phoenix Files 0.83 ☑ Exercises Assignment 1 Prove that the product of two even. functions is even And the product of two odd fos is is even. 2) Prove that if f(x) is even, then | f(x)l, f(x) {ƒ³) are even. 3) If f(x) is old, show that (f(x)) and f(x) are even 4) If g(x) is any function defined for all x, prove that P(x)= [(x) +9(-x)] is even and is odd, and g(x) = P()+q(x). q=[-(-)] 5 Determine whether the following functions old or neither: are even c) f(x) = x/x), (ii) f(x) = |x|, (iii) f(x) = x³ for 5x52 -14440 x² -1
10:00 AM < Photo.pdf Phoenix Files 0.83 ☑ Exercises Assignment 1 Prove that the product of two even. functions is even And the product of two odd fos is is even. 2) Prove that if f(x) is even, then | f(x)l, f(x) {ƒ³) are even. 3) If f(x) is old, show that (f(x)) and f(x) are even 4) If g(x) is any function defined for all x, prove that P(x)= [(x) +9(-x)] is even and is odd, and g(x) = P()+q(x). q=[-(-)] 5 Determine whether the following functions old or neither: are even c) f(x) = x/x), (ii) f(x) = |x|, (iii) f(x) = x³ for 5x52 -14440 x² -1
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![10:00 AM
<
Photo.pdf
Phoenix Files
0.83
☑
Exercises
Assignment 1
Prove that the product of two even.
functions is
even
And the product
of
two odd
fos is
is even.
2) Prove that if f(x) is even, then | f(x)l, f(x) {ƒ³)
are
even.
3) If f(x) is old, show that (f(x)) and f(x)
are even
4) If g(x) is any function defined for all x, prove that
P(x)= [(x) +9(-x)] is
even
and
is odd, and g(x) = P()+q(x).
q=[-(-)]
5 Determine whether the following functions
old or neither:
are even
c) f(x) = x/x), (ii) f(x) = |x|, (iii) f(x) = x³ for 5x52
-14440
x² -1<x<0
0≤x<1,
xx<
1,
-24×4-1
f(x) =
(vii)
1, -2<x<-1
-x,
-15×40
f(x)=
0, -1<x<1
x₁ 0≤x≤1
1,
<1x<2
15×<2
6) Evaluate (1) Cos 2, Sin 1, (c) Cas(-1), Sio (-51)
(ii) Cos5π, Sinsπ7, (iv) tam 77, (1) tan
4
Evaluate the
Dim 2
0
Rotate
Assignment 2
following limits:
20) (②2) lim (x+3)(x-4)
Search
Share
| |||
n](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe661eb0b-0d50-4c76-891e-f18c8fb0f228%2F22040d82-422b-43ce-b96a-2b5b40457af6%2Ff2jof1u_processed.jpeg&w=3840&q=75)
Transcribed Image Text:10:00 AM
<
Photo.pdf
Phoenix Files
0.83
☑
Exercises
Assignment 1
Prove that the product of two even.
functions is
even
And the product
of
two odd
fos is
is even.
2) Prove that if f(x) is even, then | f(x)l, f(x) {ƒ³)
are
even.
3) If f(x) is old, show that (f(x)) and f(x)
are even
4) If g(x) is any function defined for all x, prove that
P(x)= [(x) +9(-x)] is
even
and
is odd, and g(x) = P()+q(x).
q=[-(-)]
5 Determine whether the following functions
old or neither:
are even
c) f(x) = x/x), (ii) f(x) = |x|, (iii) f(x) = x³ for 5x52
-14440
x² -1<x<0
0≤x<1,
xx<
1,
-24×4-1
f(x) =
(vii)
1, -2<x<-1
-x,
-15×40
f(x)=
0, -1<x<1
x₁ 0≤x≤1
1,
<1x<2
15×<2
6) Evaluate (1) Cos 2, Sin 1, (c) Cas(-1), Sio (-51)
(ii) Cos5π, Sinsπ7, (iv) tam 77, (1) tan
4
Evaluate the
Dim 2
0
Rotate
Assignment 2
following limits:
20) (②2) lim (x+3)(x-4)
Search
Share
| |||
n
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