lim x->0 sinx/x
To find the limit of sinx/x as x approaches 0, we can use the concept of L’Hôpital’s Rule
To find the limit of sinx/x as x approaches 0, we can use the concept of L’Hôpital’s Rule.
L’Hôpital’s Rule states that if we have a limit of the form 0/0 or ±∞/±∞, then taking the derivative of the numerator and denominator separately can help us to determine the limit.
In this case, we have the limit of sinx/x as x approaches 0, which is of the form 0/0. So, let’s apply L’Hôpital’s Rule.
First, we take the derivative of the numerator and denominator separately. The derivative of sinx with respect to x is cosx, and the derivative of x with respect to x is 1.
Now, the limit can be expressed as:
lim x->0 sinx/x = lim x->0 cosx/1
As x approaches 0, cosx approaches 1. Therefore, we have:
lim x->0 cosx/1 = 1/1 = 1
So, the limit of sinx/x as x approaches 0 is 1.
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