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

Problem

(lim_x→0)(ƒ(x))

Solution

1. Identify the goal, which is to find the value that the function ƒ(x) approaches as the input x gets closer and closer to 0

2. Check if the function ƒ(x) is continuous at x=0 If it is, the limit can be found by direct substitution.

3. Substitute x=0 into the expression for ƒ(x) if the function is defined and continuous at that point.

4. Analyze indeterminate forms like 0/0 or ∞/∞ if they occur, using algebraic manipulation, factoring, or L'Hôpital's Rule to resolve the limit.

5. Evaluate the left-hand limit (lim_x→0)(ƒ(x)) and the right-hand limit (lim_x→0)(ƒ(x)) to ensure they are equal, which is necessary for the general limit to exist.

Final Answer

(lim_x→0)(ƒ(x))=ƒ(0)

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