Is this the right answer?

"Approximate: sqrt.(99.8)"

Any and all help is greatly appreciated!

Question

Is this the right answer?

"Approximate: sqrt.(99.8)"

Any and all help is greatly appreciated!

freckles · Answer

you know sqrt(100)

amonoconnor · Answer

Yes! :)

freckles · Answer

so I suggest doing linerzation for f(x)=sqrt(x) at x=100

anonymous · Answer

9.98

freckles · Answer

first step to do this is find the tangent line at x=100
$$y-f(100)=f'(100)(x-100) \ y=f'(100)(x-100)+f(100)$$

freckles · Answer

this equation could be a pretty close approximation for values near x=100
and 99.8 is pretty close to 100

amonoconnor · Answer

Right, that's what I did, I just wanted to make sure I did it right. It's been a bit lols;) 
I got 9.99 with the Linearization formula dealio. Is that close enough to the actual answer?

freckles · Answer

$$\sqrt{x} \approx f'(100)(x-100)+f(100) \text{ for values near } x=100$$

freckles · Answer

yep it should be in that ball park it should be something pretty close to 10
which is what you got

freckles · Answer

but I'm going to see what I get using the equation I have above

freckles · Answer

yep I got 999/100 as well which is 9.99

amonoconnor · Answer

Sweet!! Thanks a zillion;)

freckles · Answer

putting it into the calculator gives me 9.989994...
which is pretty damn close to what we got

amonoconnor · Answer

Heck yes it is... sounds good to me:)