Expert: Paul Klarreich - 11/21/2009

Question
QUESTION: sir
I have a mathmetical problem in limit and continuty in calculas.
so i'd be greatful to you for ur solution.

The qstn is

Lim x→0 {(sinx°)/x} =?   


ANSWER: Questioner: akkha
Country: Nepal
Category: Calculus
Private: No
Subject: mathmetical problem
Question: sir
I have a mathmetical problem in limit and continuty in calculas.
so i'd be greatful to you for ur solution.

The qstn is

Lim x→0 {(sinx°)/x} =?   
......................................
It is equal to 1.  See any standard calculus book for the proof.



---------- FOLLOW-UP ----------

QUESTION: the answer is 1 when we take limit X tends to Zero and the function F(x) si equal to sinx/x where x is in radian.

but in my question the x is given in Degree.
and teh given answer is  (Pie/180) where pie is in radian.
so plz i m waiting ur answer...
hope to get ur suitable solution. so plz refer my 1st qstn.

Answer
Lim x→0 {(sinx°)/x} =?   

ANSWER: Questioner: akkha
Country: Nepal
Category: Calculus
Private: No
Subject: mathmetical problem
Question: sir
I have a mathmetical problem in limit and continuty in calculas.
so i'd be greatful to you for ur solution.

The qstn is

Lim x→0 {(sinx°)/x} =?   
......................................
It is equal to 1.  See any standard calculus book for the proof.



---------- FOLLOW-UP ----------

QUESTION: the answer is 1 when we take limit X tends to Zero and the function F(x) si equal to sinx/x where x is in radian.

but in my question the x is given in Degree.
and teh given answer is  (Pie/180) where pie is in radian.
so plz i m waiting ur answer...
hope to get ur suitable solution. so plz refer my 1st qstn.


So you mean:
    sin( degree equivalent of x)
lim  ----------------------------- =
         x

[You really should refuse to do examples involving degrees.  Degrees are for children.]

    sin( 180 x/pi)
lim  ----------------
         x

Let Y = 180 x/pi,  then x = pi Y/180

and when x -> 0, so does Y.


    sin( Y )
lim  ------------
    pi Y/180

    180 sin( Y )
lim  ------------
       pi Y

180       sin( Y )
--- lim  ---------
pi          Y

180
--- (1)
pi

180
---
pi