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

Problem

(lim_x→0)(x)*cos(x)

Solution

1. Identify the type of limit by substituting the value x=0 into the expression.

2. Substitute the value 0 for x in the first factor of the product.

x=0

3. Substitute the value 0 for x in the second factor of the product.

cos(0)=1

4. Multiply the results of the two factors to find the limit.

0⋅1=0

Final Answer

(lim_x→0)(x)*cos(x)=0

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