5. Prove the trignometric identity cos20=2cos² 0 - 1 using the identities discussed in class and use it show that cos=√√+2
5. Prove the trignometric identity cos20=2cos² 0 - 1 using the identities discussed in class and use it show that cos=√√+2
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
5
![5. Prove the trignometric identity cos20=2cos² 0 - 1 using the identities discussed in class and use it
show that cos=√√+₂
V
6. Determine the one-sided limits at c= 1, 2, and 4 of the function g(x) shown in the following figure,
and state whether the limit exists at each of these points.
y
tar
(a) lim
x-1
√E-1
x-1
(e) lim
I→∞
/9x4+3x+2
4x³+1
1
3
7. Estimate the following limits numerically or state that the limit does not exist. If infinite, state
whether the one-sided limits are +
or -∞.
3
(a) lim x=0
x-0
2
1
(a) f(x) = -
(b) lim
x 3
2
x³2x²-9
T2 - 2x - 3
8. Verify each limit using the definition of limit.
(b) lim 7x - 4 = 10
x 2
(f) lim [2x]
1-
x-2
+
4 5
X
x-4
x 4√√√√8-T
(c) lim
(g) lim
4(x-4)3
(c) lim 3x²+x=4
x →0
9. Find the vertical and horizontal asymptotes of the following functions.
9x² - 4
2x²-x
(b) f(x)=x²-3x4
x-1
(d) lim
x →1
3 I
T 1
(h) lim +
I →→∞ I +1
(d) lim √x = 2
x 4](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb4251c5c-a463-4606-b15d-fe5df5ea0545%2Fe36ea221-9096-4b32-bec4-1d532b8a9d37%2Famqfhuo_processed.jpeg&w=3840&q=75)
Transcribed Image Text:5. Prove the trignometric identity cos20=2cos² 0 - 1 using the identities discussed in class and use it
show that cos=√√+₂
V
6. Determine the one-sided limits at c= 1, 2, and 4 of the function g(x) shown in the following figure,
and state whether the limit exists at each of these points.
y
tar
(a) lim
x-1
√E-1
x-1
(e) lim
I→∞
/9x4+3x+2
4x³+1
1
3
7. Estimate the following limits numerically or state that the limit does not exist. If infinite, state
whether the one-sided limits are +
or -∞.
3
(a) lim x=0
x-0
2
1
(a) f(x) = -
(b) lim
x 3
2
x³2x²-9
T2 - 2x - 3
8. Verify each limit using the definition of limit.
(b) lim 7x - 4 = 10
x 2
(f) lim [2x]
1-
x-2
+
4 5
X
x-4
x 4√√√√8-T
(c) lim
(g) lim
4(x-4)3
(c) lim 3x²+x=4
x →0
9. Find the vertical and horizontal asymptotes of the following functions.
9x² - 4
2x²-x
(b) f(x)=x²-3x4
x-1
(d) lim
x →1
3 I
T 1
(h) lim +
I →→∞ I +1
(d) lim √x = 2
x 4
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