Linearization problems.

Whateverchan

Whateverchan

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Oct 18, 2013
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Can someone explain to me how to do these two problems? My idiot teacher couldn't explain a single thing, the textbook instructed me some nonsense and told me to use a calculator, other sources on the internet were too complicated. I don't even know where to start. :-x


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Whateverchan said:
Can someone explain to me how to do these two problems? My idiot teacher couldn't explain a single thing, the textbook instructed me some nonsense and told me to use a calculator, other sources on the internet were too complicated. I don't even know where to start. :-x


View attachment 3330
Click to expand...
Your files are not readable - too small. Let me say a little about linearization, using calculus. The intent is to make a straight line approximation to a portion of a non-linear equation. If you have a nonlinear f(x), and you evaluate the function AND its first derivative at x=a, then

\(\displaystyle f(x) \approx f(a) + (x - a)\ f'(a)\)

Is that what you are working on? Show us your work, so we can see what the question really is, and also can see where you are getting stuck.
 
I know how to do a normal problem with that function, but this is different. It's square root 4 of 1+2x about equal to 1+1/2x. I am supposed to determine the value of x within 0.1

The second problem is delta x and y. y = square root x, x = 1, and delta x = 1. I found dy, but I don't know what delta x is and I have to graph it. How can I show my work if I have no idea where to start? Maybe you could give me some hints to get started.
 
The text in the graph appears to be as follows.

Verify the given linear approximation at a = 0. Then determine the values of x for which the linear approximation is accurate to within 0.1. Round your interval-notation answer to three decimal places.

. . . . .\(\displaystyle \sqrt[4]{1\, +\, 2x}\, \approx\, 1\, +\, \frac{1}{2}x\)

Compute \(\displaystyle \Delta\, y\) and dy for the given values of x and dx = \(\displaystyle \Delta\, x\). Round your answer to three decimal places.

. . . . .\(\displaystyle y\, =\, \sqrt{x},\, x\, =\, 1,\, \Delta\, x\, =\, 1\)
 
As Dr.Phil had suggested, start with calculation of \(\displaystyle \frac{dy}{dx}\) and show us what you get.
 
stapel said:
The text in the graph appears to be as follows.

Verify the given linear approximation at a = 0. Then determine the values of x for which the linear approximation is accurate to within 0.1. Round your interval-notation answer to three decimal places.

. . . . .\(\displaystyle \sqrt[4]{1\, +\, 2x}\, \approx\, 1\, +\, \frac{1}{2}x\)

Compute \(\displaystyle \Delta\, y\) and dy for the given values of x and dx = \(\displaystyle \Delta\, x\). Round your answer to three decimal places.

. . . . .\(\displaystyle y\, =\, \sqrt{x},\, x\, =\, 1,\, \Delta\, x\, =\, 1\)
Click to expand...

First one: I think that I have to put 4sqrt(1+2x) - 0.1 < 1+1/2x < 4sqrt(1+2x) + 0.1. I don't know what else to do after that.

Second one: I found y' = 1/2 (x)^-1/2, since x = 1, I just plugged it in. I don't know how to find delta y or graph them.
 
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