13 - AverageValue

# 13 - AverageValue - r on the interval[e e d Ex Find the...

This preview shows pages 1–6. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Average Value Suppose we want to find the average temperature over a 24 hour period. We will take n measurements so Average temperature = T ( t 1 ) T ( t 2 ) ... T ( t n ) n Since the more measurements we take the better the approximation, we will rewrite this expression as a Riemann sum over 0 ≤ t ≤ 24. Recall that t 24 n ±±so±± n 24 t . Average temperature = T ( t 1 ) T ( t 2 ) ... T ( t n ) 24 t = 1 24 T ( t 1 ) + T ( t 2 ) + ... + T ( t n ) t = 1 24 T ( t i i 1 n Δ t lim n 1 24 T ( t i Δ t i 1 n 1 24 T ( t dt 0 24 In general the average value of f from a to b is 1 b - a f ( x dx a b
Ex. Find the average value of f(x) = (x – e)

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

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.

Unformatted text preview: r on the interval [e, e+d]. Ex. Find the average value of f ( x ) cos x 3 8 x 2 3 on [0, 8]. Do: Find the average value of f ( x ) 2 x-3 3 on [1, 4]. Mean Value Theorem: If f is continuous on [a, b], there exists a number c in [a, b], such that f ( c ) 1 b-a f ( x )± dx a b . Ex. f(x) = x 2-1 ≤ x ≤ 1 Ex. f(x) = (x – e) r [e, e + d] Ex. f ( x ) 1 x ±±±±±±[1, 3]...
View Full Document

## This note was uploaded on 10/16/2009 for the course MATH 1206 taught by Professor Llhanks during the Spring '08 term at Virginia Tech.

### Page1 / 6

13 - AverageValue - r on the interval[e e d Ex Find the...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online