Consider the function f: R--> R where π1 , π2 β β If π is continuous at π₯β¦
2026
Consider the function f: R--> R
where π1 , π2 β β
If π is continuous at π₯ = 0, then π1 + π2 = _________.
Answer: 3 β For x β€ 0, f(x) = 3, so f(0) = 3 and the left-hand limit at 0 is 3. For x > 0, f(x) = cβeΛ£ - cβ ln(1/x). As x β 0+, ln(1/x) β β. For the right-hand limit toβ¦
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Correct answer: 3
For x β€ 0, f(x) = 3, so f(0) = 3 and the left-hand limit at 0 is 3. For x > 0, f(x) = cβeΛ£ - cβ ln(1/x). As x β 0+, ln(1/x) β β. For the right-hand limit to be finite, cβ must be 0. Then the right-hand limit becomes cβeβ° = cβ. Continuity at x = 0 requires cβ = 3. Therefore cβ + cβ = 3 + 0 = 3.
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