# Limits and continuity, differentiation, integration, homework help

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### Question Description

6 questions

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## Tutor Answer

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

Surname 1

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Professor

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1. Determine whether the following functions are continuous

In order to determine if a function is continuous at a point π₯ = π , 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. π(π₯) = {

π₯ β 2, π₯ < 1

π₯β₯1

βπ₯,

When π₯ = 1, π(π₯) = π₯ β 2 πππππππ 1 β 2 = β1 πππ π(π₯) = βπ₯ πππππππ β1 = 1

The solutions are not equal hence the function is not continuous.

1

π₯ πππ π₯ < 2

0 πππ

b. π(π₯) =

1

π₯=2

1

{

1 β π₯ πππ π₯ > 2

Surname 2

1

1

1

1

1

π€βππ π₯ < 2 , π(π₯) = 2 π€βππ π₯ = 2 , π(π₯) = 0 πππ π€βππ π₯ > 2 , π(π₯) = 2 hence the function

is not continuous.

2. Find the differential of the following

a. π(π₯) = 100π₯ 4 + 8π₯ 3 β π₯ 2 + 24π₯ β 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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