Let f:R → R be differentiable at a and let f' (a)= 2. Let (a,) be a sequence of positive terms converging to 0. Define the sequence (X,) as follows: For each natural number n, let f(a+3a,)-f(a) -2an Then the sequence (X,): Select one: O a. converges to -3 O b. converges to -1/2 O c. may not converge O d. converges to -2

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.1: Infinite Sequences And Summation Notation
Problem 72E
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Let f:R → R be differentiable at a and let f (a)=2. Let (a,) be a sequence of
positive terms converging to 0. Define the sequence (X,) as follows: For each natural
number n, let
f(a+3a,)-f(a)
Xn
%3D
-2a,
Then the sequence (X,):
Select one:
O a. converges to -3
b. converges to -1/2
O c. may not converge
d. converges to -2
Transcribed Image Text:Let f:R → R be differentiable at a and let f (a)=2. Let (a,) be a sequence of positive terms converging to 0. Define the sequence (X,) as follows: For each natural number n, let f(a+3a,)-f(a) Xn %3D -2a, Then the sequence (X,): Select one: O a. converges to -3 b. converges to -1/2 O c. may not converge d. converges to -2
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