Q. 9 what it means, in terms of limit... [FREE SOLUTION]

Chapter 10: Q. 9 (page 777)

what it means, in terms of limits, for a function to have a removable discontinuity, a jump discontinuity, or an infinite discontinuity at x = c

Short Answer

Expert verified

If limit $\lim_{x 鈫� c} f (x) 鈮� f (c)$ then the discontinuity is known as removable discontinuity.

If limit $\lim_{x 鈫� c^{-}} f (x) 鈮� \lim_{x 鈫� c^{+}} f (x)$ then the discontinuity is known as jump discontinuity.

If limit $\lim_{x 鈫� c^{-}} f (x) = 鈭� o r \lim_{x 鈫� c^{+}} f (x) = 鈭�$ then the discontinuity is known as infinite discontinuity.

Step by step solution

Step 1. Given information.

A function has a removable discontinuity, a jump discontinuity, or an infinite discontinuity at $x = c .$

Step 2. removable discontinuity.

A function is discontinuous at $x = c$ if its limits as role="math" localid="1648280454491" $x 鈫� c$ is not equal to the function value at $x = c$ and this type of discontinuity is known as removable discontinuity.

$\lim_{x 鈫� c} f (x) 鈮� f (c)$

Step 3. Jump discontinuity.

A function is discontinuous if its left limit and right limit are not equal and this type of discontinuity is known as jump discontinuity.

$\lim_{x 鈫� c^{-}} f (x) 鈮� \lim_{x 鈫� c^{+}} f (x)$

Step 4. infinite discontinuity.

A function is discontinuous if its graph has vertical or horizontal asymptotes so that its left limit or right limit or both is equal to infinity.

$\lim_{x 鈫� c^{-}} f (x) = 鈭� o r \lim_{x 鈫� c^{+}} f (x) = 鈭�$

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what it means, in terms of limits, for a function to have a removable discontinuity, a jump discontinuity, or an infinite discontinuity at x = c

Short Answer

Step by step solution

Step 1. Given information.

Step 2. removable discontinuity.

Step 3. Jump discontinuity.

Step 4. infinite discontinuity.

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