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Find the domain of the function. $ g(x) = \dfr…

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Problem 5 Medium Difficulty

Find the domain of the function.

$ f(x) = \dfrac{\cos x}{1 - \sin x} $


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Jeffrey Payo

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Calculus 1 / AB

Calculus 2 / BC

Calculus 3

Calculus: Early Transcendentals

Chapter 1

Functions and Models

Section 2

Mathematical Models: A Catalog of Essential Functions

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Integration Techniques

Partial Derivatives

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cosx /1+ sinx find the interval of increase

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Multivariate Functions - Intro

A multivariate function is a function whose value depends on several variables. In contrast, a univariate function is a function whose value depends on only one variable. A multivariate function is also called a multivariate expression, a multivariate polynomial, a multivariate series, or a multivariate function of several variables.

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12:15

Partial Derivatives - Overview

In calculus, partial derivatives are derivatives of a function with respect to one or more of its arguments, where the other arguments are treated as constants. Partial derivatives contrast with total derivatives, which are derivatives of the total function with respect to all of its arguments.

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Video Transcript

let's find the domain of this function. So if we were just looking at a coastline function, it's domain would be all real numbers. And if we were just looking at a sine function, it's domain would be all real numbers. However, here we have a denominator with one minus sign of X, and we know we can't divide by zero. That's undefined. So we need to figure out what would make one minus sign of X equal to zero and then exclude those numbers from the domain. So let's solve this equation for X. So if this is true, then sign of X would be one. And we want to figure out what angles have assigned value of one X is the inverse sign of one. So I'm going to think about my unit circle and on the unit circle. The X coordinate of the point is the co sign and the Y coordinate of the point is the sign. So up at pi over two radiance. We have assigned value of one because we have the 10.1 and nowhere else on the unit circle. Do we have that? However, we could go all the way around a circle again and back to that, so we would be adding to pie. So the original one is pi over two. And if we add two pi to that, we get five pi over two. And if we had to part of that, we get nine pi over two, etcetera. There will be infinitely many. So the way we can describe that is we can say that X is high over to plus two pi times in where two Pi represents going all the way around the circle and end represents any integer so you could go all the way around the circle once all the way around the serval twice and so on. So these are the numbers that we can't have in the domain. So we need to say what is in the domain, and that's pretty tricky. So instead of saying what is in the domain, we're going to say what is not so The domain is the set of X values, so that X is a real number, and X is not equal too high or too plus two pion

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Related Topics

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Oregon State University

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Boston College

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Lectures

Video Thumbnail

04:31

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A multivariate function is a function whose value depends on several variables. In contrast, a univariate function is a function whose value depends on only one variable. A multivariate function is also called a multivariate expression, a multivariate polynomial, a multivariate series, or a multivariate function of several variables.

Video Thumbnail

12:15

Partial Derivatives - Overview

In calculus, partial derivatives are derivatives of a function with respect to one or more of its arguments, where the other arguments are treated as constants. Partial derivatives contrast with total derivatives, which are derivatives of the total function with respect to all of its arguments.

Join Course
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