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Let $ f(x) = \frac {x}{\sqrt{1 - \cos 2x}} $(a) Graph $ f. $ What type of discontinuity does it appear to have at $ 0? $(b) Calculate the left and right limits of $ f $ at $ 0. $ Do these values confirm your answer to part (a)?

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00:53

Frank Lin

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 3

Derivatives of Trigonometric Functions

Derivatives

Differentiation

Missouri State University

Oregon State University

Baylor University

Boston College

Lectures

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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.

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In mathematics, a differentiation rule is a rule for computing the derivative of a function in one variable. Many differentiation rules can be expressed as a product rule.

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(a) find each point of dis…

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(a) By graphing the functi…

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Determine the points of di…

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find the points of discont…

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yet square. So when you read here, so we have f of X is equal to X over square it of one minus co sign two x When we draw this it looked something like this and you see that there is a jump discontinuity at zero part B. We're gonna be focusing on the bottom part. We're gonna use the trick identity for a double angle co sign only, get one minus co sign of two X is equal to one minus one minus two. Signed square, which is equal to two signs square. When we calculate the dirt, the limit as X goes to the positive side of zero for X over square of one minus co. Sign two acts. This becomes equal to the limit as X approaches zero positive for X over square root of to sign square root of to sign Sign of X, which is equal to one over square root of two limit as X approaches. Zero positive of X. Over sign of X. This is equal to one over square root of two. This is from the right side, so it's gonna be positive. And when we find the derivative the limit. Excuse me. Um, since it's gonna be from the left side, it's gonna be negative.

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