Posted by Abi on Wednesday, February 9, 2011 at 9:59pm.
Use the graph to estimate the limit:
lim x>0 sin(3x)/x
When x is in degrees
lim x>0 sin(3x)/x = ________
I thought the the answer was (3*180)/pi but it's not... please help... Thanks

Calculus  MathMate, Wednesday, February 9, 2011 at 10:12pm
Use Lim x>0 sin(x)/x =0
The proof can be done using the sandwich (squeeze) theorem.
Expand
sin(3x)
=3cos²(x) sin(x)sin³(x)
=sin(x)(3cos²(x)1+(1sin²(x)))
=sin(x)(3cos²(x)1+cos²(x))
=sin(x)(4cos²(x)1)
As x>0, cos(x)>1, so the limit becomes
Lim x>0 3sin(x)/x
=3 Lim x>0 sin(x)/x
The latter limit can be quoted as a standard limit, or can be proven using the sandwich theorem.

Calculus  Abi, Wednesday, February 9, 2011 at 10:18pm
The first value I tried was 3... and it didn't work either, I thought that the fact that it said "x is in degrees" affected. It also said at the end: (Give your answer accurate to at least 0.01...

Calculus  MathMate, Wednesday, February 9, 2011 at 11:33pm
Sorry, I am used to working with radians without thinking when dealing with limits and calculus. I have not properly read the instructions (would be fatal in exams!).
To change from degrees to radians, we need to multiply the number of degrees by %pi;/180, so the problem in radians is really:
Lim x>0 sin(3x*π/180)/x
=Lim x> sin(πx/60)/x
=π/60
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