Question

Find the limit

Answer 1

\[\lim_{x \rightarrow ?1}\frac{ (x^2-1)(\sin(3x-3)) }{\cos(x^3-1)(Tan^2(x^2-x)) }\]

Answer 2

It should say Lim x---> 1

Answer 3

I am not allowed to use L'hopitals rile. rule*

Answer 4

I am not sure how to simplify this. I can't rationalize and I dont see any apparant trignometric identities.

Answer 5

you'll have to make use of this :
firstly substitute x-1 --> 0 or y--> where y = x-1

now you must know
y->0 sin y /y = 1
and
y->0 tan y /y = 1

hope that'll help..

Answer 6

That didn't make sense...

Answer 7

Where did you get the x-1 from?

Answer 8

x --> 1 right?
or in other words,

x-1 --> 0

wasnt any miracle !! o.O

Answer 9

Ohh...

Answer 10

haha...

Answer 11

So I got:

Answer 12

Now what? @shubhamsrg .

Answer 13

Can I substitute 0 for x-1?