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Is the function defined by $f(x)=\left\{\begin{array}{ll}\frac{1}{x} & \text { if } x \neq 0 \\ 1 & \text { if } x=0\end{array} \text { continuous at (a) } x=2 ?\right.$(b) $x=0 ?$

(a) yes(b) no

03:17

Manisha S.

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

Boston College

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.

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In the question we have to prove that the function Fx is equal to X to the power and is continuous at X equals to win where and is a positive interior. Now moving towards the solution for the given function affects equal stretch to the power and we have to check continued tiered X equal student. So limit extending to win. FfX will be cool to limit extending to win X to the power current. So putting an in place often you will get into the government. Now we will be finding F off and so it will also give us and to the power and now as your limit and the function give the same value. So your given function, F X is continuous. Act x equals two. and thank you.

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