Question

I need math help plz

Answer 1

What did i do wrong??? Plz only gimme hints. Thanks

Answer 2

Plz only give me hints. Thanks

Answer 3

Instead of multiplying it by sqrt(x) - 2
try multiply it by sqrt(x) + 2


Since (a - b)(a + b) = a^2 - b^2

Answer 4

Omg... i think i found the damn mistake... i forgot to change the signs.. /.-

Answer 5

lol

Answer 6

Brb...let me see if i can solve this solve..

Answer 7

So far so good?

Answer 8

And can i take x and 4 common out from both numerator and denominator???

Answer 9

So far so good.
No you can't take x and 4 out of the numerator and denominator because they're being added/subtracted not multiplied.

Answer 10

:/ k i need a hint at this point

Answer 11

Oh my gook... let me distribute the thing brb

Answer 12

Do i need to factor the numerator and denominators?

Answer 13

I think you went off track there...

Answer 14

But can i get to the same answer with this tho ?

Answer 15

no

Answer 16

How were you able to cancel out the root in the denominator?

Answer 17

Omg... i thought they had opposite signs.. /.- good catch bro

Answer 18

Is it time to plugin the value of x now ?

Answer 19

I’m gonna invest some time to figure out an easier way to solve these type of questions later..

Answer 20

The denominator can be simplified further.

Answer 21

Apply FOIL or the distributive property

Answer 22

Sorry... i made a mistake... i’m Here right now..

Answer 23

Hero.. i’ll Explore that method in a bit mate.. gimme a minute to finish this question bro

Answer 24

K so do i just plugin the value of x now ?

Answer 25

Omg... if i plugin x = 4 for x .... i get in trouble

Answer 26

Wait, let me post a final picture of my solution just so we’re on the right page :)

Answer 27

The answer is 1/4

Answer 28

ye

Answer 29

But if i plugin 4 for x...i get a 0 in the numerator

Answer 30

You haven't finished reducing the denominator

Answer 31

or the numerator for that matter

Answer 32

Wait, really? I’m doing the whole question again to see if i made a mistake and .... anyways..

Answer 33

Do we need to factor the numerator and denominator?

Answer 34

isn't it obvious

Answer 35

Omg /.-

Answer 36

lol

Answer 37

Bless your soul for that... cuz i wan’t gonna guess that in 9 eternities..

Answer 38

Boom!

Answer 39

Thank you so much guys.. the next three limit questions are interrelated to one another.. it’s super weird

Answer 40

Let me take a picture of that thing.. brb

Answer 41

It’s from 8,9, and 10

Answer 42

Ah yes

Answer 43

What do i plugin from question 8 into question 9/?? The answer?

Answer 44

Why’re questions 8,9 and 10 so similar? Are they high. ?

Answer 45

What do they mean by (use the results from question 8 and 9?

Answer 46

So here's the definition of a limit:

\[\lim_{x \rightarrow a}f(x) = b\]
if
\[\lim_{x \rightarrow a^{+}}f(x) = b\]
and
\[\lim_{x \rightarrow a^{-}}f(x) = b\]

Answer 47

What does that *+* and *-* mean???

Answer 48

+ means from the right
- means from the left


In this diagram, the limit at 'a' approaches 'b' from the right, and 'c' from the left

Answer 49

Since 'b' and 'c' do not equal, then the limit at 'a' does not exists.

Answer 50

Ok let me just do the questions first.. and see if that confirms it

Answer 51

Hey, so you're right on the fact that the limit of x approaching 1 of 3/(x-1) is DNE, but your left hand and right hand limits are wrong.

Left hand and right hand limits must be evaluated using logic sometimes. Algaebraically it doesn't always work.

The limit of x approaching 1 from the right is infinity, and from the left is negative infinity. For a limit to exist, the right and left hand limits must be the same. Since one is positive infinity and the other is negative infinity, THAT's why it's DNE.

Answer 52

Logically, for the limit of x approaching 1 from the right, the denominator keeps getting smaller and smaller. Imagine plugging in 1000, then 100, then 10, then 1.1, then 1.0001. The denominator gets smaller. When that happens, the number is larger, and larger, all the way to infinity! So the answer for that is infinity

Answer 53

And from the left, apply the same concept. You're at -1000, then -100, then -10, then -1.1, and -1.000000001. So the number is getting more negative and negative...toward negative infinity. So the limit of x approaching 1 from the left is negative infinity.

Answer 54

He's right.
Take a look at the graph:
https://www.desmos.com/calculator/dw4lsng8ej

Answer 55

I got it. Thanks pal.