or the textbook,In the previous assignment, you created a piecewise function to model the income tax due basedon a given level of income. If we extend the endpoints to interpret any real number input, wearrive at the following function for the tax due based on an income of x dollars.f(x) =. 10x,.12(x-9950) +995,.22(x-40,525) + 4,664,.24(x86,375) +14,751,.32(x - 164,925) +33,603,.35(x - 209,425) + 47,843,37(x - 523,600) + 157,804.25,1. Find the following.lim f(x)X-9950-b. lim f(x)C.lim f(x)d. f(9950)x ≤ 9,9509,950 < x≤ 40,525 w240,525 < x≤ 86,37586,375 < x≤ 164,925164,925 < x < 209,425209,425 < x < 523,600x > 523,600 2. Use your work from problem (1) to determine whether the function is continuous at x =9950. Explain.3. Show that the function is also continuous/not continuous at x = 40,525.4. Based on your work from above, on what interval(s) do you expect the function to becontinuous. Note the domain carefully.

As per the guidelines I am supposed to do the first question among multiple questions, still I am…

he textbook, an the previous assignment, you created a piecewise function to model the income tax due based a given level of income. If we extend the endpoints to interpret any real number input, we rive at the following function for the tax due based on an income of x dollars. f(x) = .10x, .12(x-9950) +995, .22(x-40,525) + 4,664, .24(x86,375) +14,751, .32(x-164,925) +33,603, .35(x - 209,425) + 47,843, 37(x - 523,600) + 157,804.25, 1. Find the following. lim f(x) a. X-9950- b. lim f(x) C. lim f(x) d. f(9950) x ≤ 9,950 9,950 < x≤ 40,525 2 40,525 < x≤ 86,375 86,375 < x≤ 164,925 164,925 < x < 209,425 209,425 < x < 523,600 x > 523,600

he textbook, an the previous assignment, you created a piecewise function to model the income tax due based a given level of income. If we extend the endpoints to interpret any real number input, we rive at the following function for the tax due based on an income of x dollars. f(x) = .10x, .12(x-9950) +995, .22(x-40,525) + 4,664, .24(x86,375) +14,751, .32(x-164,925) +33,603, .35(x - 209,425) + 47,843, 37(x - 523,600) + 157,804.25, 1. Find the following. lim f(x) a. X-9950- b. lim f(x) C. lim f(x) d. f(9950) x ≤ 9,950 9,950 < x≤ 40,525 2 40,525 < x≤ 86,375 86,375 < x≤ 164,925 164,925 < x < 209,425 209,425 < x < 523,600 x > 523,600

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Question

or the textbook,
In the previous assignment, you created a piecewise function to model the income tax due based
on a given level of income. If we extend the endpoints to interpret any real number input, we
arrive at the following function for the tax due based on an income of x dollars.
f(x) =
. 10x,
.12(x-9950) +995,
.22(x-40,525) + 4,664,
.24(x86,375) +14,751,
.32(x - 164,925) +33,603,
.35(x - 209,425) + 47,843,
37(x - 523,600) + 157,804.25,
1. Find the following.
lim f(x)
X-9950-
b. lim f(x)
C.
lim f(x)
d. f(9950)
x ≤ 9,950
9,950 < x≤ 40,525 w2
40,525 < x≤ 86,375
86,375 < x≤ 164,925
164,925 < x < 209,425
209,425 < x < 523,600
x > 523,600

2. Use your work from problem (1) to determine whether the function is continuous at x =
9950. Explain.
3. Show that the function is also continuous/not continuous at x = 40,525.
4. Based on your work from above, on what interval(s) do you expect the function to be
continuous. Note the domain carefully.

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