Explain why or why not Determine whether the following state-ments are true and give an explanation or counterexample.cosh (In 3)da.dr-(sinh (In 3)) =3ddb.-(sinh x) = cosh x and (cosh x) = -sinh x.drdxc. In(1 + V2) = -In(-1+ V2).%3Ddrd.Jo 4 – x2co

a) Let y=sinhln3 Differentiate y with respect to x, dydx=ddxsinhln3=0 Using…

Answered: Explain why or why not Determine…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.7: Applications

Problem 18EQ

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Question

Explain why or why not Determine whether the following state-
ments are true and give an explanation or counterexample.
cosh (In 3)
d
a.
dr
-(sinh (In 3)) =
3
d
d
b.
-(sinh x) = cosh x and (cosh x) = -sinh x.
dr
dx
c. In(1 + V2) = -In(-1+ V2).
%3D
dr
d.
Jo 4 – x2
co

Expert Solution

Step 1

Let $y = \sin h (\ln 3)$

Differentiate y with respect to x,

$\begin{array}{rcl} \frac{d y}{d x} & = & \frac{d}{d x} (\sin h (\ln 3)) \\ = & 0 [U \sin g \frac{d}{d x} C = 0, w h e r e C i s a c o n s \tan t t e r m] \end{array}$

Hence

$\begin{array}{rcl} \frac{d}{d x} (\sin h (\ln 3)) & = & \frac{\cos h (\ln 3)}{3} \end{array}$ not true.

Step 2

b) We know that

$\frac{d}{d x} (\sin h x) = \cos h x A n d \frac{d}{d x} (\cos h x) = \sin h x$

Hence

$\frac{d}{d x} (\sin h x) = \cos h x i s t r u e .$

And $\frac{d}{d x} (\cos h x) = - \sin h x$ is not true.

Hence $\frac{d}{d x} (\sin h x) = \cos h x a n d \frac{d}{d x} (\cos h x) = - \sin h x$ is not true.

Step by step

Solved in 3 steps

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Explain why or why not Determine whether the following state- ments are true and give an explanation or counterexample. cosh (In 3) d a. dr -(sinh (In 3)) = 3 d d b. -(sinh x) = cosh x and (cosh x) = -sinh x. dr dx c. In(1 + V2) = -In(-1+ V2). %3D dr d. Jo 4 – x2 co