Question

The equation below has a solution near x = 0. By replacing the left side of the equation by its linearization, find an approximate value for the solution. Note: Your answer should be in fraction form.

e^x+14x+7

Answer 1

First of all, we'll need an equation. Otherwise,"solution" has no meaning. Did you mean

e^x + 14x + 7 = 0

?

Maybe something else.

Answer 2

well i guess thats means the same right?

Answer 3

so i find the linearization of that?

Answer 4

near x+0? or near =7?

Answer 5

No, not at all. Language and terminology are importaant. It enables us to communicate with each other.

This is an expression:

e^x+14x+7

This is an Equation:

e^x+14x+7 = 0

Well, 14x + 7 is already linear, so all we need to focus on is the e^x. How do you find the "linearization" of e^x around x - 0?

Answer 6

The problem statement says there is a solution around x = 0.

Answer 7

1x+1

Answer 8

right?

Answer 9

How did you get that? Is there a derivative in there and your just not sharing your secret?

Answer 10

f'(a)(x-a)+f(a)

Answer 11

local linearization formula

Answer 12

You have it. Then the linearization of the entire left-hand side is what?

Answer 13

1x+1?

Answer 14

No, that's just e^x. The linearization of e^x is 1+x around x = 0, as we have established.

This gives (1+x) + 14x + 7 as the linearization of the entire left-hand side.

Answer 15

and now what?

Answer 16

i'm lost

Answer 17

The point of linearization is to make the evaluation of the function easier, understanding that we introduce a little error. Unfortunately, we don't quite know the original problem on this one.

For x = 0, we have e^0 + 14(0) + 7 = 1 + 0 + 7 = 8

For the linearization, we have (1+0) + 14(0) + 7 = 8

For that, we introduced no error.

Now, we need to know the original problem statement in its entirety. What is the original equation?