# Linear Approximation problem

#### Fyou88

Estimate using differentials.

sin(0.00001)

#### mr fantastic

MHF Hall of Fame
Estimate using differentials.

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

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

#### Fyou88

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

#### mr fantastic

MHF Hall of Fame
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.

#### Fyou88

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

#### mr fantastic

MHF Hall of Fame
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.

#### Fyou88

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

Last edited:

#### mr fantastic

MHF Hall of Fame
how do u know that x will be = 0? anyone help please??
Go back and review the examples in your class notes or textbook.

#### Fyou88

Estimate

e^sqrt0.0001

I already know how to do e^0.0001.

#### mr fantastic

MHF Hall of Fame
e^sqrt0.0001

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

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