Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Explain, using Theorems 4, 5, 7, and 9, why the function is continuous at every number in its domain. State the domain.

$ B(x) = \dfrac{\tan x}{\sqrt{4 - x^2}} $

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

05:53

Daniel Jaimes

05:49

Linda Hand

Calculus 1 / AB

Chapter 2

Limits and Derivatives

Section 5

Continuity

Limits

Derivatives

Missouri State University

Harvey Mudd College

University of Michigan - Ann Arbor

Boston College

Lectures

04:40

In mathematics, the limit of a function is the value that the function gets very close to as the input approaches some value. Thus, it is referred to as the function value or output value.

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.

0:00

Explain, using Theorems 4,…

01:52

03:47

05:22

03:44

04:57

05:24

07:33

$25-32$ Explain, using The…

02:18

So in this problem we are given this function Vfx is tangent of X divided by the square root of form honest. X squared were asked to use the rooms 457 and nine to show that B of X is continuous. And the state the domain for B. Fx. So first of all, bye there. I'm seven attention X is continuous over its domain. Well, what is the domain of this? Well, first of all, the domain for tangent X. Is all the face of X. Such that X is not equal to two n Plus one. Um Spy over to where in is a natural number. Okay. Mhm. Then also by there I'm seven. The skirt of four months x squared. Yeah. Is continuous over its domain. Mm What's the domain of this? Well, let's just see the main of this is what? Well, if I put in two for X I get zero. I can do the screw to zero. Let's put something greater than two. And their let's say three, three squared is nine. So I have four minus nine. That's negative five. I can't do the screw to -5. Oh, that's interesting. So what happens if I put in negative two in here? Well, negative two squared is positive for four months. 40. Okay, so this domain then turns out to be all the real numbers between negative two and two. Inclusively in here. Okay, now then when we look at our theorems, my serum for and nine we have then that vfx is continuous over its domain. Well, what's the domain of the fx mm. Well, first of all for the denominator to not be zero or afford to be defined at all. Okay, then, I have values between minus two and two, don't I? And I can't let the denominator be zero. All right. So this means this is all the values of X. Such that X is in -2-2 without -2 and two being in there. Because those may make the denominator zero. And I can't have this denominator can't be zero. Okay. But I also can't have this right has to be valid over this domain. And what do I notice? I notice that minus pi over two and pi over two are both in here. So I need to add on to this. And also X is not equal two pi over two or minus pi over two. Because both of those show up in that ah in this interval, don't they? Okay, so there is my domain B of X. And by the theorems, provided we know that this is continuous over this domain

View More Answers From This Book

Find Another Textbook

'Example 66. Find the geometric mean of the following distribution Valu…

04:12

'a. Describe in words what features most of the frequency distributions…

02:08

'The circumference of a circle is 66 ft: a) Find the diameter of the ci…

00:52

'Where T 3.14, find the approximate area of a circle (not shown) whose …

00:59

'In excavating for a new house, the Philpott Brothers dig a hole in the…

01:21

'Find the perimeter of the rectangle.6 m16 m'

07:07

'316. The graph ofa folium of Descartes with equation 2x3 + 2y3 _ 9xy =…

02:50

'RequiredWhich of the following does not appear in a statement of c…

03:13

'For next year; David Company has budgeted sales of 8,000 units, target…

03:39

'The base x of the right triangle in the figure increases at a rate of …