Evaluate the Limit limit as x approaches 0 of 2sin(x)-1

Problem

(lim_x→0)(2*sin(x)−1)

Solution

1. Identify the type of limit. Since the function ƒ(x)=2*sin(x)−1 is a combination of a trigonometric function and a constant, it is continuous for all real numbers.

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

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

2*sin(0)−1

4. Evaluate the trigonometric value. We know that sin(0)=0

2*(0)−1

5. Simplify the resulting numerical expression.

0−1=−1

Final Answer

(lim_x→0)(2*sin(x)−1)=−1

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