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Discuss (i) the continuity and; (ii) the differentiability of the given function. (iii) If a discontinuity is removable, redefine the function so as to make it continuous there. (iv) Is it now differentiable?$$f(x)=\frac{x^{2}-2}{x-5}$$

Non rem. Disc at $x=5,$ diff everywhere except at $x=5$

Calculus 1 / AB

Chapter 2

An Introduction to Calculus

Section 3

Limits and Continuity

Derivatives

Missouri State University

Campbell University

University of Michigan - Ann Arbor

Idaho State University

Lectures

04:40

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

30:01

In mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value (the rate of change of the value of the function). If the derivative of a function at a chosen input value equals a constant value, the function is said to be a constant function. In this case the derivative itself is the constant of the function, and is called the constant of integration.

03:18

Let $f(x)=|x-1|([x]-\{x\})…

03:36

If $f^{\prime}(x)=\left\{\…

So to check the differential ability F-1 one plus equal limit Extends to one plus FX -F one Called X -1. Equal limit. Ah H tends to zero LTD it tends to zero F one plus h minus f one Upon one plus H -1. Equal limit H tends to zero which tends to do more edge the latest interior function of one plus at minus Correction part of one plus minus zero upon open edge. So limit H tends to zero when my message upon it equal one. Also also cash 1- Equal limit. X turns to one F x minus F one upon x minus one. Equal limit h tends to zero F one minus x minus f one 1 1 -1 -1 recall limit. It turns to zero one minus H zero upon minus So equal limit It turns to zero minus more. More of minus age. The test indigent function of one plus eight minus fractional part of one plus edge. Bone minus edge equal Limit which turns to 0- said into 0 -1. Plus upon minus edge Equals -1. So we can say this this fx is no different than a bullet, not two french able at X equals genius since both Both one sided 1 decided derivative exists derivative exist. No they are they are unequal So effects is continuous. Mexico Jiro

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