Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question
totor 22 answer no1 only
Transcribed Image Text:17 SECOND DERIVATIVES
TUTORIAL 22
2
dy it y = In (x² + 1), answer=
Find
dx
2. Find the second derivative of y = In ( cos 3x ).
Given that y = In ( 2 - cos x). Find and simplify
3.
Given that y = (A + x) cos x, where A is a constant, show that
4.
d'y
+y is independent of A.
dx
at the point x = 0. answer.
Given y = e* sin x. Evaluated
=e-x (cos(x+b)
d²y dy
6. If y = ae 2 sin (x + b), show that
+ 4dx
dx²
+ 5y = 0
where a and b are constants.
dy
that
prove
+4
7. If y = 3xe 2x
dx
+ 4y = 0.
dy
8. Let y = e³* sin 4x. Show that
+ 25y = 0.
dx
9. Let y = Ae* + sin x.
dy
+ y = dx
express A (constant) in terms of x.
b) Hence, evaluate A
when x = π.
ex
Find, in terms of e, the values of
X + 1
1
√x+1
show that
+
+ xy³
dx
dx
E
3 tan 3x;
10. Given that y =
at x = 1.
11. Given y =
Answers:
dx
2x
1
2 - 2x²
(x² + 11²
2.
dx
and
2x²
√√(x²
+ 1) 5
= -9 sec² 3x
MAT -
![a) If
b)
10. Given that y
at x = 1.
11. Given y =
1
Answers:
2x
2 - 2x²
=
x² + 1
+ 1)
sin x
d'y
2 cos x -
1
=
2 cos x' dx²
(2
cos x)
dy
d'y
=
dx e* (cos x - sin x);
= -2e * cos x;
dx
=
dx ae 2x [cos (x + b) - 2 sin (x + b)]
3e ²* (1 - 2x);
dx
e³x [4 cos 4x + 3 sin 4x]
d'y
dx
COS X
9b) A =
хе'
(x + 1)
4'
X
(x + 1)
3.
허증 검증 검증 검증 검증 검증 < 검증 증
dx
dx
dy
6.
7.
dy
dx
dy
8.
dx
9a) A
dx
dy
11.
dy
=
dx express A (constant) in
1
A
when x = π.
Find, in terms of e, the
*
show that
+
dx²
"1
dx²
+ y
Hence, evaluate
x + 1
+
=
=
0.0432
dx
d'y
dx
N
2.
= -3 ta
dy
dx = (A +
=-2
= ae- [3 si
dx
= 12xe 2x
12e
ex [24 cos 4x - 7 sin
e (x² + 1) e
=
(x + 1)³
2x² - 1
(x² + 1)
dy
4.
허증 검증
5/2
92](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc32ca5a9-fa89-4035-ac59-02a6d49f7e2d%2Fa601a31f-ea24-4525-a8d5-323fb16a2d5b%2F0xmvqoq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:a) If
b)
10. Given that y
at x = 1.
11. Given y =
1
Answers:
2x
2 - 2x²
=
x² + 1
+ 1)
sin x
d'y
2 cos x -
1
=
2 cos x' dx²
(2
cos x)
dy
d'y
=
dx e* (cos x - sin x);
= -2e * cos x;
dx
=
dx ae 2x [cos (x + b) - 2 sin (x + b)]
3e ²* (1 - 2x);
dx
e³x [4 cos 4x + 3 sin 4x]
d'y
dx
COS X
9b) A =
хе'
(x + 1)
4'
X
(x + 1)
3.
허증 검증 검증 검증 검증 검증 < 검증 증
dx
dx
dy
6.
7.
dy
dx
dy
8.
dx
9a) A
dx
dy
11.
dy
=
dx express A (constant) in
1
A
when x = π.
Find, in terms of e, the
*
show that
+
dx²
"1
dx²
+ y
Hence, evaluate
x + 1
+
=
=
0.0432
dx
d'y
dx
N
2.
= -3 ta
dy
dx = (A +
=-2
= ae- [3 si
dx
= 12xe 2x
12e
ex [24 cos 4x - 7 sin
e (x² + 1) e
=
(x + 1)³
2x² - 1
(x² + 1)
dy
4.
허증 검증
5/2
92
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