2. Recall that in Written Assignment #3 you showed that ifS3f(x) =if x < 0if x > 0then lim f(x) DNE.x→0(a) Is f(x) continuous at x = 0? Briefly explain your answer.(b) Now consider the functionif x < a3 -g(x) =- TXif x > aShow that there exists a value of a which makes g(x) continuous everywhere. (Hint: Drawthe graphs ofgraph of g(x) looks like y = 3 – Tx for x a. Based on the graphs,how should you choose a so that g(x) is continuous? Use the IVT to justify that there issuch a number a.)3 – Tx and yx* on the same axes. For a particular value of a, the(c) Use the Bisection Method to find the value of a accurate to one decimal place.

(a) The objective is to find whether f(x) is continuous x=0. No, f(x) does not exist in x=0 because…

(a) Is f(x) continuous at x = 0? Briefly explain your answer. (b) Now consider the function 3 – Tx if x < a g(x) = if x > a Show that there exists a value of a which makes g(x) continuous everywhere. (Hint: Draw the graphs of y = 3 – 7x and y = x* on the same axes. For a particular value of graph of g(x) looks like y = 3 – Tx for x < a and y = x4 for x > a. Based on the graphs, how should you choose a so that g(x) is continuous? Use the IVT to justify that there is such a number a.) а, the (c) Use the Bisection Method to find the value of a accurate to one decimal place.

(a) Is f(x) continuous at x = 0? Briefly explain your answer. (b) Now consider the function 3 – Tx if x < a g(x) = if x > a Show that there exists a value of a which makes g(x) continuous everywhere. (Hint: Draw the graphs of y = 3 – 7x and y = x* on the same axes. For a particular value of graph of g(x) looks like y = 3 – Tx for x < a and y = x4 for x > a. Based on the graphs, how should you choose a so that g(x) is continuous? Use the IVT to justify that there is such a number a.) а, the (c) Use the Bisection Method to find the value of a accurate to one decimal place.

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter3: Functions

Section3.3: More On Functions; Piecewise-defined Functions

Problem 99E: Determine if the statemment is true or false. If the statement is false, then correct it and make it...

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