Find limits of sine and cosine functions

In summary, the limit of (1-cos2x)/(xsinx) as x approaches 0 is 2. There may have been a textbook error regarding the expected answer of 0.
  • #1
Glissando
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0

Homework Statement


Find the limit:

lim (1-cos2x)/(xsinx)
x->0


Homework Equations


Identities


The Attempt at a Solution



I've done this over and over and over again! The answer is supposed to be 0 but I keep getting 2 ):

lim (1-cos2x)/(xsinx)
x->0

lim (1-1+2sin2x)/(xsinx)
x->0

lim (2sin2x)/(xsinx)
x->0

lim (2sinx)/x
x->0

= 2*1 = 2

Any help is appreciated! Thank you!
 
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  • #3
I don't see anything wrong with what you did. I'd say the limit is 2 as well.
 
  • #4
Thanks guys (: I guess textbook error then! Yay!

Thank you <3
 

FAQ: Find limits of sine and cosine functions

1. What is the definition of a limit of a function?

A limit of a function is the value that a function approaches as its input approaches a certain value. It represents the behavior of the function near a specific input value.

2. How do you find the limit of a sine function?

To find the limit of a sine function, you can use the fact that the limit of sin(x) as x approaches a value a is equal to sin(a). In other words, the limit of sin(x) as x approaches a is equal to the value of the sine function at a.

3. Can the limit of a sine function be undefined?

Yes, the limit of a sine function can be undefined. This can happen when the function has a vertical asymptote (a point where the function approaches infinity) or a jump discontinuity (a point where the function has a sudden change in value).

4. How do you find the limit of a cosine function?

Similar to the sine function, the limit of a cosine function can be found by simply plugging in the value that the function is approaching. So the limit of cos(x) as x approaches a is equal to cos(a).

5. What is the difference between the left and right limits of a function?

The left limit of a function at a specific point is the value that the function approaches as the input approaches that point from the left side. The right limit is the value that the function approaches as the input approaches from the right side. If the left and right limits are equal, then the overall limit exists. If they are not equal, then the limit does not exist.

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