MATH 1210 Week 3 Assignment

MATH 1210 Week 3 Assignment | Tulane University

Module 3 Quiz

Solve the problems below and write up a solution to each problem using complete English sentences and well-organized calculations as appropriate. Your solution will be graded based on mathematical accuracy and clarity of presentation.

Late submissions will not be accepted. You must submit your responses as a single .pdf file that includes all pages of your solution. You may resubmit until the deadline but only the most recent submission will be graded. Quiz submissions will not be accepted via e-mail. After submitting you must download your file to ensure that it submitted properly. See technical instructions on Module Quiz submissions.

Problem 1:

Sketch the graph of a function ffff that satisfies the following conditions. If such a function does not exist explain why.

·          limx→−1f(x)=2limx→−1f(x)=2limlim x → − 1 f ( x ) = 2

·         limx→1+f(x)=2limx→1+f(x)=2limlim x → 1 + f ( x ) = 2

·         limx→1−f(x)=4limx→1−f(x)=4limlim x → 1 − f ( x ) = 4

·         limx→3+f(x)=−1limx→3+f(x)=−1limlim x → 3 + f ( x ) = − 1

·         f(3)=0f(3)=0ff ( 3 ) = 0

·         f(1)=5f(1)=5ff ( 1 ) = 5

·         f(−1)=2f(−1)=2

Problem 2:

Find all the points where the following function is continuous:

f(x)=⎧⎩⎨x2x+1exif x<0if x>0.f(x)={x2x+1if x<0exif x>0.ff ( x ) = { x 2 x + 1 if  x < 0 e x if  x > 0 .

Does ffff have a removable discontinuity at any value x=ax=axx = a? In case ffff has a removable discontinuity at x=ax=axx = a, how would you remove the discontinuity?