1. ## Linear Approximation problem

Estimate using differentials.

sin(0.00001)

2. Originally Posted by Fyou88
Estimate using differentials.

sin(0.00001)
$f(x + h) \approx f(x) + h f'(x)$.

Use f(x) = sin(x), x = 0, h = 0.00001.

3. ok thank. if it was sin(0.9999) would x = 1 and then h=0.9999?

4. Originally Posted by Fyou88
ok thank. if it was sin(0.9999) would x = 1 and then h=0.9999?
No. If x = 1 and you require x + h = 0.9999 then h = -0.0001.

5. so it will be 0 again? and x= the value u estimating the # that is closer to?

6. Originally Posted by Fyou88
so it will be 0 again? and x= the value u estimating the # that is closer to?
I have no idea what you are referring to.

I have clearly answered both of your questions. I suggest you knuckle down to doing the calculations.

7. how do u know that x will be = 0? anyone help please??

8. Originally Posted by Fyou88
how do u know that x will be = 0? anyone help please??
Go back and review the examples in your class notes or textbook.

9. ## Estimate

e^sqrt0.0001

I already know how to do e^0.0001.

10. Originally Posted by Fyou88
e^sqrt0.0001

I already know how to do e^0.0001.
$f(x + h) \approx f(x) + h f'(x)$.

Use $f(x) = e^{\sqrt{x}}$, x = 0, h = 0.0001

11. ok.

12. so f prime (x)=e^sqrt x and e^sqrt0=1.

so m = 1 (0,1)
y-y1=m(x-x1)
y-1=1(x-0)
y=x+1

may someone help mee??

13. Originally Posted by Fyou88
so f prime (x)=e^sqrt x and e^sqrt0=1.

so m = 1 (0,1)
y-y1=m(x-x1)
y-1=1(x-0)
y=x+1

may someone help mee??
What you have posted here makes absolutely no sense - particularly in the context of this thread (which is about applying the linear approximation).

And if $f(x) = e^{\sqrt{x}}$ then your derivative is wrong. The derivative is calculated using the chain rule.

Look, the fact is that currently you're quite out of your depth with the questions you are posting - the root cause of this appears to be a poor knowledge of the pre-requisite concepts and skills. As I have previously said, you are strongly advised to go back and learn those skills properly before attempting questions that depend on knowing them. I also strongly suggest that you get remedial help from your instructor.

14. Originally Posted by Fyou88
so f prime (x)=e^sqrt x and e^sqrt0=1.
NO, you said that f(x)= e^(sqrt x). Do you know how to find the derivative of that?

so m = 1 (0,1)
y-y1=m(x-x1)
y-1=1(x-0)
y=x+1

may someone help mee??
mr. fantastic has been trying to help you but you are not doing what he told you to do.

15. e^sqrtx*1/2sqrt x?