Evaluate the limit: lim(x→0) (sin x)/x.
Solution
Problem
Evaluate the limit: lim(x→0) (sin x)/x.
Step 1: Identify the limit.
We need to evaluate:
lim(x→0) (sin x)/x
Direct substitution gives:
sin(0)/0 = 0/0
This is an indeterminate form.
Step 2: Recognize the fundamental trigonometric limit.
One of the fundamental limits in calculus is:
lim(x→0) (sin x)/x = 1
This result applies when x is measured in radians.
Step 3: Apply the fundamental limit.
Because the given expression exactly matches this standard form, the limit is 1.
Therefore:
lim(x→0) (sin x)/x = 1.
Result
1