November 3
rd
2008
Mathematics 140
Sections 3.10 & 3.11
(Linear approximations and Hyperbolic functions)
Notes:
•
Almost no one is here!
•
I miss staring at the back of your head while you concentrate and look angelic
•
Sections 3.10

Linear Approximations and Differentials

Tangent lines to curves at specific points (usually defined by “a”

Increase in function from point “a” to “x”

(Tangent line approximations)

Ex. 28 pg. 252

Use differentials (or, equiventlenty a linear approximation) to estimate the square root of
99.8

Old techniques for when we did not need calculators

First of all, what is the function?

Left f(x) be root x

Point close to 99.8 is 100 and the root is 10 (Use this information)

Need the derivation of root x

f'(x) = 1/2sqrt(x)

f(x)f(a)/(xa) is approx f'(a)

we can use this ratio as an approximation

f(x) is approx. = f(a)+f'(a)*(xa) = L(x) where L = linearisation of f

WHERE a = 11 and x = 99.8

KNOW THIS STUFF DOM DOM!

10+1/20(0.2) = close to the root of 99.8

The term DIFFERENTIAL

Precise definition which is premature of this class...
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '08
 LASKO
 Hyperbolic Functions, Hyperbolic function, Inverse hyperbolic sine

Click to edit the document details