Evaluate the Limit limit as x approaches 0 of tan(x)

Problem

(lim_x→0)(tan(x))

Solution

1. Identify the type of function. The function ƒ(x)=tan(x) is a trigonometric function that is continuous at x=0

2. Apply the direct substitution property for limits of continuous functions.

3. Substitute the value x=0 into the expression.

(lim_x→0)(tan(x))=tan(0)

4. Evaluate the trigonometric value. Since tan(0)=sin(0)/cos(0)=0/1 the result is 0

Final Answer

(lim_x→0)(tan(x))=0

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