Question

Lim (5x³-3x²+x-6)
x→6

I am instructed to expand it fully before plugging in 3 -:(

Answer 1

I did it, but just saying that MY COURSE IS A WASTE OF TIME.

Answer 2

Expand what fully??

Answer 3

Yeah :P

Answer 4

Using limit rules, like to say

5 ( Lim x ) ³ ... and on
x→6

I just have one question, will this NOT make a difference in all cases ?

Answer 5

Do you mean factor instead of expand?

Answer 6

shouldn't, using the "definition of a limit" formula as opposed to just pluging it in should give the same

Answer 7

Yeah..

Answer 8

It shouldn't matter though since you'll get 972 anyways

Answer 9

factor, like simplify it in all ways

Answer 10

I get 105

Answer 11

By simplifying and plugging in, or just by plugging in

Answer 12

not true all the time.... btw... the "definition of a limit" formula can however cancel out factors "just plugging it in" does not

Answer 13

example sir , please ?

Answer 14

but I can see the expansion woiuld be a long one =)

Answer 15

I did it on my paper, it's like each question = 1 paper, and I got about 10 of those...

Answer 16

Can you imagine how many trees....

Answer 17

lmao

Answer 18

maybe there's a wisdom to it ? =)

trees? just make them a PDF =)

Answer 19

I have to submit them in class, not online.

Answer 20

Mind checking your work again for this question?

Answer 21

Yes , sure

Answer 22

put the PDF in a usb stick and submit that, with an "ecosystem friendly" logo on it =)

Answer 23

Or just plant a tree for every assignment you hand in :P

Answer 24

Idk why your prof would make you do such a thing though

Answer 25

I am still confused, what and how you are trying to do it like??

Answer 26

Can you imagine how many trees....

Answer 27

I just cleared the reply -:(

Answer 28

\(\bf lim_{h\to 0}\quad \cfrac{f(x+h)-f(x)}{h}\leftarrow \textit{definition of a limit}\) @iambatman

Answer 29

5 ( Lim x ) ³ - 3 ( Lim x ) ² + ( Lim x ) - ( Lim 6 )
x→6 x→6 x→6 x→6


5 (3) ³ - 3 (3) ² + (3) - 6


(5 × 9)3 - (9)3 + (1)3 + (-2)3

(45 - 9 +1 -2) 3
35(3)
105

Answer 30

don't have a calculator with me

Answer 31

*cough* computer *cough*

Answer 32

It will will when I turn it off.

Answer 33

Yeah I got that jdoe :P

Answer 34

Have a good fri day (w/ pizza)

Answer 35

Why are you putting 3 there??

Answer 36

Really now ? Trying to check me ? Say so and I'll tell you

I am plugging in 3, because x approaches 3... duh !

Answer 37

3 or 6 ??

Answer 38

Iohh... I typed 6 it should be 3.

Answer 39

Sorry about that

Answer 40

I didn't recognize

Answer 41

But good that I am correct on my paper and wrong here, and not vica versa.

Answer 42

I got 105 then..

Answer 43

well, either

35(3)

or

5 (6) ³ - 3 (6) ² + (6) - 6
( 5 × 36) 6 - (18)6 + (1)6 - 6 ....

Answer 44

I can just put it into wolfram.

Answer 45

I am not just getting, you are in your question tending x to 3, but in limits, in place of x you are putting 6..

Answer 46

Kids like me always THINK they are smart when they read some about integration and other calc stuff... I must say though, that I am pretty lazy and stupid.

Answer 47

I just showed what it would be when x→6 as I errored.

Answer 48

Oh then it is okay, with x tending to 6, you will get 972..

And with 3, you get 105.

Answer 49

I didn't yet count when x→6, but for x→3 I DO get 105

Answer 50

yup 972

Answer 51

Why are you putting 3?

Answer 52

Count??

5*216 = 1080

Answer 53

I'm sort of lost on why you're doing what solomon haha...

Answer 54

I made a mistake when I typed x→6 in here, I didn't even notice it.

Answer 55

-3*36 = -108

Answer 56

OOOOH

Answer 57

It should be x→3, not x→6

Answer 58

Yeah

Answer 59

So, 1080 - 108 = ??

Answer 60

Haha, I was like I keep getting 972 no clue what you're doing, that makes much more sense xD

Answer 61

Would my teacher mind if I use L'H'S sometimes ?

Answer 62

Calc 1?

Answer 63

What is LHS now??

Answer 64

They would mark it wrong in calc 1 i'm sure

Answer 65

L'Hospitals

Answer 66

You can't use it here instead..

Answer 67

But, you can use if it is applicable in some question..

Answer 68

lim ( -1 e^(5t) ) / t
x→t

here, in this case, but I used it as an additional reason, I also made a table
like

x g(x)

and estimated plugging in approximate value as x→0^- and x→0^+

Answer 69

I mean -1+ e^(5t)

Answer 70

x tends to t??

Where is x??

Answer 71

ohh, whatever I always put in wrong variables, you know what I mean (don't you )?

Answer 72

it is just t, no Xs

Answer 73

t and g(t)

Answer 74

I know, but t tends to what??

Answer 75

I don't see it being applicable there, unless I'm wrong due to lack of sleep xD

Answer 76

Calm down. take deep breath firstly..

Now write the limits properly.. :P

Answer 77

lim ( -1 + e^(5t) ) / t
t→0

Answer 78

it is 0/0 when you plug in 0.

Answer 79

Oh haha >_>

Answer 80

This is correct now..

Answer 81

yeah...

after deriving,

5e ^ ( lim t→0 5t)

Answer 82

then I get 5

Answer 83

\[\lim_{t \rightarrow 0}- 5e^{5t} \implies -5\]

Answer 84

Sorry, +5

Answer 85

yes was just about to correct you

Answer 86

I am faster than you but slower than batman.. :P

Answer 87

Faster than me? LEts go to the gym !!!!

Answer 88

Haha, well everything make sense now?

Answer 89

after I made 500 errs

Answer 90

Yep.. You are challenging me??

Answer 91

I've never been this confused by solomon

Answer 92

You must not write on papers, you are wasting trees by the way.. :P

Answer 93

I am not challenging
I am not that good to challenge, just some annoying teenager.

Answer 94

Yeah I am, but I don't really care. I myself will have enough air

Answer 95

Then I leave you, but I would have never been left you if this were a challenge.. :P

Answer 96

Hey hey, calm down, or I'll have to intrude :P

Answer 97

Oooh Oops

Answer 98

I am scared