Subject: Calculus

Find lim x→0 sin(x)/x

The classic limit that underpins the derivative of the sine function.

Answer lim x→0 ≈ 1

Solution

Limit lim x→0 of sin(x) / x
x = -0.00001 f(x) = 1
x = -0.0001 f(x) = 1
x = -0.001 f(x) = 1
x = -0.01 f(x) = 0.999983
x = -0.1 f(x) = 0.998334
x = 0.1 f(x) = 0.998334
x = 0.01 f(x) = 0.999983
x = 0.001 f(x) = 1
x = 0.0001 f(x) = 1
x = 0.00001 f(x) = 1
Left side x→0⁻ f(x) → 1
Right side x→0⁺ f(x) → 1
Conclusion Both sides agree → limit ≈ 1

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