Linearization problems.

[Whateverchan]

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

 

[DrPhil]

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

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.

 

[Whateverchan]

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.

 

[Bob Brown MSEE]

Use Graph for first problem

CLICK HERE
and notice the x-values for which y>0.1

Answer: [-0.368, 0.677]

 

[stapel]

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.

. . . . .$\displaystyle y\, =\, \sqrt{x},\, x\, =\, 1,\, \Delta\, x\, =\, 1$

 

[Deleted member 4993]

As Dr.Phil had suggested, start with calculation of $\displaystyle \frac{dy}{dx}$ and show us what you get.

 

[Whateverchan]

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.

. . . . .$\displaystyle y\, =\, \sqrt{x},\, x\, =\, 1,\, \Delta\, x\, =\, 1$

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.

 

[Whateverchan]

Can someone help me with this one?