Limits + Trig Help NEEDED! (1 Viewer)

[blackops23]

Hi guys, need some help on 3 questions involving limits as x--> 0 for certain trig functions

I can do simple questions like lim x-->0 (sin5x)/(2x)

But here a few questions which I don't get:

Q1) lim x-->0 sin2x/tanx

Here's what I did:

2sinxcosx/(sinx/cosx)
=lim x-->0 2(cosx)^2 --> How do you find this limit? Or is there another way?

----------

Q2) lim x-->0 tan3x/sin4x

No idea how to do this!

-----------------
Q3) lim x-->0 3[(sinx)^2]/(x^2)

Once again no idea how do to this!

-----------------
Also side question:

Is this true: lim x-->0 1 + sinx = lim x-->0 1 + lim x-->0 sinx?
----------------

Also lim x-->0 sinx = x or is it equal to 0?

Thank you everyone, appreciate the help!

 

[woga3]

you cheat and do it the university way.

 

[woga3]

I remember seeing a similiar question like 2008 sydney boys trial I think.

I think there was a way to manipulate the standard trig limits, but I forgot.

nevertheless I don't really care bout helping you aye

 

[woga3]

"lim x-->0 2(cosx)^2 --> How do you find this limit?" are you serious.

some of you 4unit students are even worse than brightside. By the way, where is he lols, I want to wish him good LUCK for the trials ( especially maths )

 

[nightweaver066]

Do you know the other identity?


First question.


(changing tanx in to its identity)


Cancelling the s


Second question.





Third question.





Yes, your statement is true. You can split limits apart as long as their addition, subtraction, or even the top part of a fraction with the bottom part of a fraction.



Imagine the sine graph. As x -> 0 from either side of x, it always approaches 0.

 

[Hermes1]

Q 3)

as u can see above u manipulate the expression so u can get the simple trig limits like sin x/x and then put a number out the front which neutralises the changes u hav made.

 

[Drongoski]

But over the last 20 years or so all questions have been based on:

 

[Hermes1]

But over the last 20 years or so all questions have been based on:

have they ever asked these trig limits with an actual applied trig question, like a 3D trig question?

 

[blackops23]

Cancelling the s

Thank you very much nightweaver! and Hermes! but just a side question about solving limits in the form of the above quote.

What is the rule when doing limits involving products? I.e. for addition/subtraction you can split them, but what do you do for multiplication? Do you just find the limits for the individual terms and multiply them together?

Thanks, once again help is greatly appreciated

 

[nightweaver066]

That's for fractions. Sorry about it looking so ugly, don't know how to make it look better.

Multiplication one is the same, you can split it and take the limit for each one and multiply them together.

 

[khfreakau]

I like using l'hopital's rule. Also, imagine the graph at x=0 -> eg for q1 2cos^2x, as it approaches 0, sub in x = 0, cos^2x approaches 1. Hence, the answer is 2.1 = 2