Infinity Cross
January 26th, 2010
What is the limit as x approaches negative infinity of sin (2x) / x?
I think the answer is two using the identity that sin (2x) / 2x = 1, but when I look at the graphing calculator it looks like it is approaching 0, crossing the x-axis back and forth? Please let me know how you solved it. Thanks!
The answer is 0.
Since -1 <= sin(2x) <=1 for all x,
-1/x <= sin(2x)/x <= 1/x for all x not equal to 0.
Now let x--> – infinity. Then, since 1/x, -1/x –> 0, the squeeze law forces
sin (2x) / x –> 0.
cross my heart – Infinity Doesn’t Live Here Anymore
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