2. a. Write the precise mathematical definition of continuity. b. Explain in your own words what it means for a function to be continuous at a point. What will be some characteristics of the graph of the function? c. Suppose the function h(x) is defined as follows: [a sin (x) if x< 0 h(x)= {3 if x= 0 6-2co0s(x*) if x> 0 • Use the definition of continuity to find values of a and b that make h(x) continuous at x = 0. • Show each step of the definition of continuity, including both left and right limits.

2. a. Write the precise mathematical definition of continuity. b. Explain in your own words what it means for a function to be continuous at a point. What will be some characteristics of the graph of the function? c. Suppose the function h(x) is defined as follows: [a sin (x) if x< 0 h(x)= {3 if x= 0 6-2co0s(x*) if x> 0 • Use the definition of continuity to find values of a and b that make h(x) continuous at x = 0. • Show each step of the definition of continuity, including both left and right limits.

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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