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Given the piecewise defined function g(x) = {_-lx! + k, if x < 3 x², if x ≥ 3 what value of k makes g(x) continuous at x=3?

Given the piecewise defined function g(x) = {_-lx! + k, if x < 3 x², if x ≥ 3 what value of k makes g(x) continuous at x=3?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Recall that a function f(x) is continuous at a value x = a if 1. the limit of f(x) as x approaches a exists 2. the limit of f(x) as x approaches a equals f(a). Given the piecewise defined function 8(x) = {1x! + k, if x < 3 x², if x ≥ 3 what value of k makes g(x) continuous at x=3?
Transcribed Image Text:Recall that a function f(x) is continuous at a value x = a if 1. the limit of f(x) as x approaches a exists 2. the limit of f(x) as x approaches a equals f(a). Given the piecewise defined function 8(x) = {1x! + k, if x < 3 x², if x ≥ 3 what value of k makes g(x) continuous at x=3?
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