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**Unformatted text preview: **Math 2215 Chapter 4 Notes Fall 2015.notebook October 16, 2019 Find the limit of s(n) as n→ ∞ (note: n is an integer but thms about x →∞ where x is real still hold) Calc notes Math 2215 Chapter 4 Notes Fall 2015.notebook October 16, 2019 Find a formula for the sum of n terms then use the formula to find the limit as n → ∞ Calc notes Math 2215 Chapter 4 Notes Fall 2015.notebook October 16, 2019 Math 2215 Chapter 4 Notes Fall 2015.notebook October 16, 2019 Archimedes Method of Exhaustion Calc notes Math 2215 Chapter 4 Notes Fall 2015.notebook October 16, 2019 Upper and Lower Sums
Consider a plane region bounded above by the graph of a nonnegative continuous function y=f(x), bounded below by the x‐axis, and to the left and right by the vertical lines x=a and x=b.
To approximate the area of the region:
Subdivide the interval [a,b] into subintervals each of length ∆x=(b‐a)/n, let f(mi) be the minimum value of f(x) in the ith subinterval and f(Mi) be the maximum value of f(x) in the ith subinterval. Define the lower sum = s(n) =
and the upper sum = S(n) = so that s(n) ≤area of region ≤ S(n) Calc notes Math 2215 Chapter 4 Notes Fall 2015.notebook October 16, 2019 Find the upper and lower sums of the region given by on [0,2] with n=8 Calc notes Math 2215 Chapter 4 Notes Fall 2015.notebook October 16, 2019 y=3x – 4 [2,5] Calc notes Math 2215 Chapter 4 Notes Fall 2015.notebook October 16, 2019 f(y) = y2 [0,3] Calc notes ...

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