Limits and continuity, differentiation, integration, homework help

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Limits and continuity, differentiation, integration, homework help
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Limits and continuity, differentiation, integration, homework help
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Limits and continuity, differentiation, integration, homework help
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MrClyneHelp
School: UC Berkeley

there you go, all questions are explained and I believe the question is fully answered

Surname 1

Name
Professor
Course
Date

1. Determine whether the following functions are continuous
In order to determine if a function is continuous at a point π‘₯ = π‘Ž , three conditions need
to be satisfied.
i.

the function f is defined at a,

ii.

the limit of f as x approaches a from the right-hand and left-hand limits exist and are
equal,

iii.

the limit of f as x approaches a is equal to f(a).

If any of the conditions is not met the function is not continuous.

a. 𝑓(π‘₯) = {

π‘₯ βˆ’ 2, π‘₯ < 1
π‘₯β‰₯1
√π‘₯,

When π‘₯ = 1, 𝑓(π‘₯) = π‘₯ βˆ’ 2 π‘π‘’π‘π‘œπ‘šπ‘’π‘  1 βˆ’ 2 = βˆ’1 π‘Žπ‘›π‘‘ 𝑓(π‘₯) = √π‘₯ π‘π‘’π‘π‘œπ‘šπ‘’π‘  √1 = 1
The solutions are not equal hence the function is not continuous.
1

π‘₯ π‘“π‘œπ‘Ÿ π‘₯ < 2
0 π‘“π‘œπ‘Ÿ

b. 𝑓(π‘₯) =

1

π‘₯=2
1

{

1 βˆ’ π‘₯ π‘“π‘œπ‘Ÿ π‘₯ > 2

Surname 2

1

1

1

1

1

π‘€β„Žπ‘’π‘› π‘₯ < 2 , 𝑓(π‘₯) = 2 π‘€β„Žπ‘’π‘› π‘₯ = 2 , 𝑓(π‘₯) = 0 π‘Žπ‘›π‘‘ π‘€β„Žπ‘’π‘› π‘₯ > 2 , 𝑓(π‘₯) = 2 hence the function
is not continuous.

2. Find the differential of the following
a. 𝑓(π‘₯) = 100π‘₯ 4 + 8π‘₯ 3 βˆ’ π‘₯ 2 + 24π‘₯ βˆ’ 8
In this case, bring the power of x down and multiply by the coefficient of x then reduce the
power by one and sinc...

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Anonymous
Excellent job

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