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## #1 2021-06-10 13:00:26

nycmathguy
Member
Registered: 2021-06-02
Posts: 53

### Investigate Each Limit

Use either a graph or a table to investigate each limit.

1. limit of sqrt{| x | - x} as x tends to 2 from the left.

2. limit of cuberoot{[ x ] - x}》as x tends to 2 from the left.

Note:

For question 1 in the radicand, we have the absolute value of x minus x.

For question 2 in the radicand, we have the step function [ x ] minus x.

I prefer the table method. What values of x can I use for each function as x tends to 2 from the left side?

Last edited by nycmathguy (2021-06-10 13:03:03)

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## #2 2021-06-11 00:41:10

Bob
Registered: 2010-06-20
Posts: 9,207

### Re: Investigate Each Limit

hi

For question 1, you can start with x = 1.9  There's no need to go near negative values as we want to approach x = 2 and so there's no need for the absolute function at all.

Just treat this as sqrt(x-x)

If you look here http://www.mathwords.com/f/floor_function.htm

and compare with http://www.mathwords.com/c/ceiling_function.htm

you'll see that two graphs are possible and it makes a difference to the limit.

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

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## #3 2021-06-11 09:15:39

nycmathguy
Member
Registered: 2021-06-02
Posts: 53

### Re: Investigate Each Limit

Bob wrote:

hi

For question 1, you can start with x = 1.9  There's no need to go near negative values as we want to approach x = 2 and so there's no need for the absolute function at all.

Just treat this as sqrt(x-x)

If you look here http://www.mathwords.com/f/floor_function.htm

and compare with http://www.mathwords.com/c/ceiling_function.htm

you'll see that two graphs are possible and it makes a difference to the limit.

Bob

I am not too familiar with the step function. I will check out the links.

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