Evaluate the Limit limit as x approaches 0 of 4sin(x-1)

Problem

(lim_x→0)(4)*sin(x−1)

Solution

1. Identify the type of function. The function ƒ(x)=4*sin(x−1) is a composition of a linear function and a sine function, both of which are continuous everywhere.

2. Apply the direct substitution property for limits of continuous functions. Since the function is continuous at x=0 the limit is equal to the value of the function at that point.

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

4*sin(0−1)

4. Simplify the expression inside the sine function.

4*sin(−1)

5. Apply the odd function property of sine, which states sin(−θ)=−sin(θ) to rewrite the expression if desired.

−4*sin(1)

Final Answer

(lim_x→0)(4)*sin(x−1)=−4*sin(1)

Want more problems? Check here!