Classify the discontinuities of f as removable, jump, or infinite. f(x)={ x^2-1 if x<1

step 1 Hi, in this video we are going to classify the discontinuities of this function. We have the fun

Classify the discontinuities of f as removable, jump, or...

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Key Concepts

Discontinuity Classification

This concept involves categorizing points where a function is not continuous, analyzing whether the discontinuity is removable, jump, or infinite. Removable discontinuities occur when the limit exists but the function is either not defined at that point or has a value different from the limit. Jump discontinuities occur when the left-hand and right-hand limits exist but do not coincide, and infinite discontinuities arise when one or both of these limits diverge to infinity.

Piecewise Functions

A piecewise function is defined by different expressions over separate intervals of its domain. The analysis of such functions focuses on the points where the definition changes, as these are potential candidates for discontinuities. Studying these transition points helps in determining how the behavior of the function changes across different segments.

One-Sided Limits

One-sided limits, including left-hand and right-hand limits, are used to evaluate the behavior of a function as it approaches a specific point from the left or the right. These limits are essential in identifying the type of discontinuity at a boundary point; if the two limits are unequal, the discontinuity is classified as a jump discontinuity, while equal limits might indicate a removable discontinuity if the function’s value does not match the limit.

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