limit as x approaches 0: sinx/x
To evaluate the limit as x approaches 0 for sin(x)/x, we can employ the concept of limits in calculus
To evaluate the limit as x approaches 0 for sin(x)/x, we can employ the concept of limits in calculus.
First, let’s simplify the expression. We know that sin(x)/x is an indeterminate form of 0/0 as x approaches 0.
Using a trigonometric identity, we can rewrite sin(x) as x times the limit of (sin(x)/x) as x approaches 0, which gives us:
lim(x -> 0) [x * (sin(x)/x)]
Simplifying further, we find:
lim(x -> 0) (sin(x)/x) = lim(x -> 0) sin(x)
Now, we can evaluate the limit of sin(x) as x approaches 0. In trigonometry, we know that sin(0) = 0, so the limit as x approaches 0 of sin(x) is 0.
Therefore, the final answer is:
lim(x -> 0) (sin(x)/x) = 0
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