Concept explainers
(a)
To sketch:The graph of the continuous function.
(a)
Explanation of Solution
Given information:
A continuous function that is
Graph:
The sigma function is defined as the function which has the value -1for the negative argument and 0 when the argument is 0 and 1 for the positive argument.
The graph for the given continuous function
Interpretation:
From the graph it is obtained that the value -1 has negative argument and 1 has positive argument. The graph is increasing and decreasing with respect to the argument value.
(b)
To find:The formula for the function.
(b)
Answer to Problem 27E
The formula for the function is given below as,
Explanation of Solution
Given information:
A continuous function that is
Calculation:
To determine the formula for the function as follows,
Consider the slope for (0.1.l) as 10, and the linear function for
The formula for the function is given below as,
(c)
The input have to be to 0 for the output to be within 0.1 for 0.
(c)
Answer to Problem 27E
The input should be within -0.01 to 0.01 for the output to be within 0.1 to 0.
Explanation of Solution
Given information:
A continuous function that is
Calculation:
The given function is
To determine the input at
Similarly, consider
From the two values of
Hence, the input should be within -0.01 to 0.01 for the output to be within 0.1 to 0.
Want to see more full solutions like this?
Chapter 2 Solutions
Modeling the Dynamics of Life: Calculus and Probability for Life Scientists
- Determine if the statemment is true or false. If the statement is false, then correct it and make it true. If the function f increases on the interval -,x1 and decreases on the interval x1,, then fx1 is a local minimum value.arrow_forwardIf a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local extremum offon (a,c) ?arrow_forwardLet f and g be functions. (a) The function (f+g)(x) is defined for all values of x that are in the domains of both _______ and_______. (b) The function (fg)(x) is defined for ail values of x that are in the domains of both ________ and_________ . (c) The function (f/g)(x) is defined for all values of x that are in the domains of both ________and________, and g(x) is not equal to ________.arrow_forward
- College Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage LearningFunctions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage LearningBig Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin Harcourt
- College AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage