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1. Let f(x) be a continuous function on [a, b], where a, b = R and a < b. Suppose that there are two sequences (xn) and (yn) satisfying that (a) a

1. Let f(x) be a continuous function on [a, b], where a, b = R and a < b. Suppose that there are two sequences (xn) and (yn) satisfying that (a) a

College Algebra
College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter3: Functions
Section3.3: Rates Of Change And Behavior Of Graphs
Problem 43SE: Let f(x)=1x . Find the number b such that the average rate of change off on the interval (2,b) is...
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. Let f (x) be a continuous function on [a, b], where a, b ∈ R and a < b. Suppose that there are two sequences
(xn) and (yn) satisfying that
(a) a < xn < c < yn < b for all n ∈ N, and
(b) lim(xn) = c and lim(yn) = c.
 REFER TO PICTURE AND PROVE IT, WHILE ALSO EXPLAINING EACH STEP IN FULL DETAIL

1. Let f(x) be a continuous function on [a, b], where a, b = R and a < b. Suppose that there are two sequences (xn) and (yn) satisfying that (a) a <n<c< Yn <b for all n = N, and (b) lim(xn) =c and lim(yn): = C. Prove that if f(x) is differentiable at c, then f(yn) - f(xn) lim = = f'(c). n→∞ Yn - xn
Transcribed Image Text:1. Let f(x) be a continuous function on [a, b], where a, b = R and a < b. Suppose that there are two sequences (xn) and (yn) satisfying that (a) a <n<c< Yn <b for all n = N, and (b) lim(xn) =c and lim(yn): = C. Prove that if f(x) is differentiable at c, then f(yn) - f(xn) lim = = f'(c). n→∞ Yn - xn
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