In the proof of + 1), arcsinh x = In (x + / -00 Thus: [6] + [7]x – [8] = 0 K e-2y Multiply with [9] ey F L e-y sinh x M sinh y N arcsinh x arcsinh y U 3 е2у — 2хеу — 1 — 0 Solving the quadratic equation: ey = x ± Vx² + 1 Note that e[10] 0. Since x [11] Vx² + 1 it follows that ey = x + Vx² + 1. Therefore: y = In([12]) = ln(x + vx²+1) That shows that arcsinh x = In(x + Vx² + 1) + OPORSTU ABCDEEC
In the proof of + 1), arcsinh x = In (x + / -00 Thus: [6] + [7]x – [8] = 0 K e-2y Multiply with [9] ey F L e-y sinh x M sinh y N arcsinh x arcsinh y U 3 е2у — 2хеу — 1 — 0 Solving the quadratic equation: ey = x ± Vx² + 1 Note that e[10] 0. Since x [11] Vx² + 1 it follows that ey = x + Vx² + 1. Therefore: y = In([12]) = ln(x + vx²+1) That shows that arcsinh x = In(x + Vx² + 1) + OPORSTU ABCDEEC
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
![In die bewys van
arcsinh x = In
,-00 < x < ∞
(I + 2x^ + x) u]-
is daar by sekere stappe ontbrekende inligting.
Voltooi die bewys deur die korrekte LETTER uit die tabel te kies.
ANTWOORDOPSIES
[3]-[4]
H
y
-y
J
Laat y = arcsinh x + [1]
sinh[2]
volgens die definisie van
=
2
-X
-2
[5]
>
Q
e2y
Dus: [6] + [7]x – [8] = 0
K
e-2y
Vermenigvuldig met [9]
ey
L
e-y
%3D
arcsinh x
arcsinh y U
— е2у — 2хеу — 1 —D 0
F
sinh x M
sinh y N
+
Deur die kwadratiese vergelyking op te los volg:
ey = x ± Vx² + 1
Let op dat e [10] 0. Aangesien x [11] Vx² + 1 is, volg dit dat
e = x + Vx2 +1
Dus: y = In([12]) = In(x + vx² + 1)
Dit volg dus dat: arcsinh x = In(x + Vx2 + 1)
In the proof of
arcsinh x = In (x
x2
+ 1
-00 <x < 0
some of the information is omitted in some of the steps.
Complete the proof by choosing the correct LETTER from the table.
ANSWER OPTIONS
[3]–[4]
according to the definition of| A
H.
y
-y
J
Let y = arcsinh x +[1] =
sinh[2]
2
В
-X
-2
[5]
>
Q
e2y
Thus: [6] + [7]x – [8] = 0
D
K
e-2y
Multiply with [9]
E
ey
L
e-y
%3D
arcsinh x
arcsinh y U
—е2у — 2хеу — 1 —D 0
F
sinh x
sinh y N
+
Solving the quadratic equation:
ey = x + Vx² + 1
Note that ey[10] 0. Since x [11] Vx2 +1 it follows that
ey = x + Vx2 + 1.
Therefore: y = In([12]) = ln(x + Vx² + 1)
That shows that arcsinh x = In(x + Vx² + 1)
SOPORSTU
OPORSTU
ABCDEEC](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F530b5701-25d1-4feb-9d9f-b49d1e97d628%2Fe1ffb616-bd31-4d9d-912a-86f8a898ca84%2Fxxy9od6_processed.png&w=3840&q=75)
Transcribed Image Text:In die bewys van
arcsinh x = In
,-00 < x < ∞
(I + 2x^ + x) u]-
is daar by sekere stappe ontbrekende inligting.
Voltooi die bewys deur die korrekte LETTER uit die tabel te kies.
ANTWOORDOPSIES
[3]-[4]
H
y
-y
J
Laat y = arcsinh x + [1]
sinh[2]
volgens die definisie van
=
2
-X
-2
[5]
>
Q
e2y
Dus: [6] + [7]x – [8] = 0
K
e-2y
Vermenigvuldig met [9]
ey
L
e-y
%3D
arcsinh x
arcsinh y U
— е2у — 2хеу — 1 —D 0
F
sinh x M
sinh y N
+
Deur die kwadratiese vergelyking op te los volg:
ey = x ± Vx² + 1
Let op dat e [10] 0. Aangesien x [11] Vx² + 1 is, volg dit dat
e = x + Vx2 +1
Dus: y = In([12]) = In(x + vx² + 1)
Dit volg dus dat: arcsinh x = In(x + Vx2 + 1)
In the proof of
arcsinh x = In (x
x2
+ 1
-00 <x < 0
some of the information is omitted in some of the steps.
Complete the proof by choosing the correct LETTER from the table.
ANSWER OPTIONS
[3]–[4]
according to the definition of| A
H.
y
-y
J
Let y = arcsinh x +[1] =
sinh[2]
2
В
-X
-2
[5]
>
Q
e2y
Thus: [6] + [7]x – [8] = 0
D
K
e-2y
Multiply with [9]
E
ey
L
e-y
%3D
arcsinh x
arcsinh y U
—е2у — 2хеу — 1 —D 0
F
sinh x
sinh y N
+
Solving the quadratic equation:
ey = x + Vx² + 1
Note that ey[10] 0. Since x [11] Vx2 +1 it follows that
ey = x + Vx2 + 1.
Therefore: y = In([12]) = ln(x + Vx² + 1)
That shows that arcsinh x = In(x + Vx² + 1)
SOPORSTU
OPORSTU
ABCDEEC
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