Find limx → 0 f(x) where, f(x) = { x - 2 for x < 0 { 0 for x = 0 { x + 2 for x
Question
Find limx → 0 f(x) where, f(x) = { x - 2 for x < 0 { 0 for x = 0 { x + 2 for x
Solution
The limit of a function as x approaches a certain value is the value that the function approaches as x gets closer and closer to that value. In this case, we are asked to find the limit as x approaches 0 for the piecewise function f(x) = {x - 2 for x < 0, 0 for x = 0, x + 2 for x > 0}.
Step 1: Find the limit as x approaches 0 from the left (x < 0). For this part of the function, f(x) = x - 2. As x gets closer and closer to 0 from the left, f(x) gets closer and closer to -2.
Step 2: Find the limit as x approaches 0 from the right (x > 0). For this part of the function, f(x) = x + 2. As x gets closer and closer to 0 from the right, f(x) gets closer and closer to 2.
Step 3: Compare the two limits. If the limit from the left does not equal the limit from the right, then the overall limit as x approaches 0 does not exist. In this case, the limit from the left is -2 and the limit from the right is 2, so the overall limit as x approaches 0 does not exist.
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