- #1

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**lim x-> 00 sin(1/x)x^2/(2x-1)???**

lim x-> 00 sin(1/x)x^2/(2x-1)???

Iv tried sandwich theorem, l'hopitals and i seem to be going nowhere

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- Thread starter cos(e)
- Start date

- #1

- 27

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lim x-> 00 sin(1/x)x^2/(2x-1)???

Iv tried sandwich theorem, l'hopitals and i seem to be going nowhere

- #2

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Maybe you could use the small angle approximation for sin? (sin(y) = y for small y)

- #3

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But that just makes sin(1/x)=0 which doesnt help, when i graph it i get the limit 1/2 i just dont know how to find it using limit laws

- #4

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You're not applying the small angle approximation. sin(y)=y for small y. I didn't say sin(y)=0 for small y.

- #5

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Oh i see that works, but im not too sure if i am meant to use the small angle approximation, but otherwise thanks

- #6

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Really? I mean it's just an approximation of the taylor series for sin(x). Seems fair game for a calculus class. Sorry I can't be of more help.

- #7

Gib Z

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Personally I don't enjoy justifying that taking sin y = y was accurate enough. It was obvious for cos(e) to question why we were not letting sin y = 0 - You have to take the correct number of terms of the series, and taking more terms until you get the expected answer really isn't good enough imo.

I would have used the Sandwich theorem with [tex] x - \frac{x^3}{6} \leq \sin x \leq x[/tex].

- #8

HallsofIvy

Science Advisor

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Since we know that

[tex]\lim_{x\rightarrrow 0}\frac{sin(x)}{x}= 1[/itex]

I would be inclined, as a first step, to let y= 1/x. Then the limit becomes

[tex]\lim_{y\rightarrow 0}\frac{sin(y)}{y^2(2/y- 1)}[/tex]

which, multiplying one of the y's from y

[tex]\lim_{y\rightarrow 0}\frac{sin y}{y}\frac{1}{2-y}[/itex]

which should be pretty easy.

- #9

statdad

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Just a question: does "x -> 00" mean the limit as x goes to zero or as x goes to infinity?

- #10

Gib Z

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[tex]\lim_{x\rightarrrow 0}\frac{sin(x)}{x}= 1[/itex]

I would be inclined, as a first step, to let y= 1/x. Then the limit becomes

[tex]\lim_{y\rightarrow 0}\frac{sin(y)}{y^2(2/y- 1)}[/tex]

which, multiplying one of the y's from y^{2}into the parentheses, gives

[tex]\lim_{y\rightarrow 0}\frac{sin y}{y}\frac{1}{2-y}[/itex]

which should be pretty easy.

A very elegant solution Halls =]

Just a question: does "x -> 00" mean the limit as x goes to zero or as x goes to infinity?

It means the limit as x goes to infinity, commonly used notation on forums for those who don't use latex.

- #11

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derivation to funkton

f(x)= e^sin^22x when x=pi/2

i try but i get "0"... is this right solution?

plz if any one help me

- #12

Mark44

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Please start a new thread rather than tacking your question onto a thread that is more than two years old.

f(x)= e^sin^22x when x=pi/2

i try but i get "0"... is this right solution?

plz if any one help me

- #13

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Please start a new thread rather than tacking your question onto a thread that is more than two years old.

com an man im not so used by sympols in com puter .. but i well try

- #14

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calculate the derivative of the function. specify the exact answer

f(x)= e^sin^2(2x) when x=∏/2

- #15

Mark44

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I wasn't talking about the symbols - don't use this thread for an unrelated problem. Please start a

- #16

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Please start a new thread rather than tacking your question onto a thread that is more than two years old.

I wasn't talking about the symbols - don't use this thread for an unrelated problem. Please start anewthread.[/QUO

heheh okok sorry i got u......

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