L’Hospital’s Rule: Finding the Limit of sin(x)/x as x Approaches 0

sinx/x (lim x -> 0)

To find the limit of sin(x)/x as x approaches 0, we can use the concept of L’Hospital’s rule

To find the limit of sin(x)/x as x approaches 0, we can use the concept of L’Hospital’s rule. L’Hospital’s rule allows us to differentiate the numerator and denominator separately and then take the limit again.

Let’s take the derivative of the numerator and denominator:

d/dx(sin(x)) = cos(x)
d/dx(x) = 1

Now, let’s apply L’Hospital’s rule:

lim x->0 (sin(x)/x) = lim x->0 (cos(x)/1)

Since the limit of cos(x) as x approaches 0 is 1, the limit of sin(x)/x as x approaches 0 is also 1.

Therefore, lim x->0 (sin(x)/x) = 1.

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