UIUC HW for Math 220, Exercises of Calculus

HW GS 4 UIUC MATH 220 HW for gradescope

Typology: Exercises

2023/2024

Uploaded on 11/28/2024

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Math 220 Fall 2024
Gradescope Homework 4
Due Monday, September 23 by 11:59pm
Refer to the “Homework” page in Canvas for assignment directions.
1. Find the value of cthat makes the function fcontinuous on (1,1). Justify your answer using the definition
of continuity.
f(x)=8
<
:
cx22xif x<2
x3+cx if x2
c=
pf2

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Math 220 Fall 2024

Gradescope Homework 4

Due Monday, September 23 by 11:59pm

Refer to the “Homework” page in Canvas for assignment directions.

  1. Find the value of c that makes the function f continuous on (1, 1 ). Justify your answer using the definition

of continuity.

f (x) =

cx 2 2 x if x < 2

x 3 + cx if x 2

c =

  1. Compute the following limits. Show sucient work to justify each answer.

(a) lim x!

5 x 2 x 3 + 3

2 x + 4x 3

(b) lim x!

p 4 x 4 2 5 x 2 + 6x