Lesson Find the range of f(x) = (5*cos(x))/(x + 1)), x >=0
Algebra
->
Customizable Word Problem Solvers
->
Misc
-> Lesson Find the range of f(x) = (5*cos(x))/(x + 1)), x >=0
Log On
Ad:
Over 600 Algebra Word Problems at edhelper.com
Word Problems: Miscellaneous Word Problems
Word
Solvers
Solvers
Lessons
Lessons
Answers archive
Answers
Source code of 'Find the range of f(x) = (5*cos(x))/(x + 1)), x >=0'
This Lesson (Find the range of f(x) = (5*cos(x))/(x + 1)), x >=0)
was created by by
ikleyn(52943)
:
View Source
,
Show
About ikleyn
:
<H2>Find the range of f(x) = {{{(5*cos(x))/(x + 1))}}}, x >= 0</H2> <H3>Problem 1</H3>Find the range of f(x) = {{{(5*cos(x))/(x + 1))}}}, x >= 0. <pre> I will show here two ways to find the range. First way is to use plotting tool like DESMOS, which you can find at the site https://www.desmos.com/calculator/ Print there the formula of the function, and you will get the plot immediately. Click on the plot somewhere around the first minimum of the function in the domain x >= 0. The plotting tool will show you the coordinates of the minimum. They are (x,y) = (2.88997,-1.24488). So, the minimum value of the function in the domain x >= 0 is -1.24488 (approximately). Thus the range is [ {{{-1.24488}}}, {{{infinity)}}} ). I saved the plot under this link https://www.desmos.com/calculator/9x4t38gmur for documentation purposes, so you can see it at any time. To see the coordinates of the minimum of the function, click on the plot in vicinity of the minimum. Another way to find the range is to find the minimum of the function in the domain x >= 0 using Calculus. Take the derivative of the function and equate it to zero. You will get an equation tan(x) = {{{-1/(x+1)}}}. It can not be solved analytically, but can be solved numerically. Use an online calculator for solving transcendent equations https://www.wolframalpha.com Print there this equation tan(x) = {{{-1/(x+1)}}}. The calculator will get you a series of the roots. Your root is the first positive number in this series x = 2.88997 (approximately). To get the minimum of the function {{{(5*cos(x))/(1+x)}}}, substitute x = 2.88997 into the function. You will get the value -1.24488 for this minimum. So, the range of the function is [ {{{-1.24488}}}, {{{infinity)}}} ), which is the same as we found it in the first solution. </pre> Thus the problem solved completely in two ways for your better understanding. My other lessons on Calculus word problems at this site are - <A HREF=https://www.algebra.com/algebra/homework/word/misc/A-ladder-foot-slides-on-the-ground-txt.lesson>A ladder foot slides on the ground</A> - <A HREF=https://www.algebra.com/algebra/homework/word/misc/Finding-rate-of-change-of-some-processes.lesson>Finding rate of change of some processes</A> - <A HREF=https://www.algebra.com/algebra/homework/word/misc/Find-the-derivative-of-a-function-defined-by-complicated-expression.lesson>Find the derivative of a function defined by complicated expression</A> - <A HREF=https://www.algebra.com/algebra/homework/word/misc/Taking-derivative-of-a-function-which-is-defined-implicitly.lesson>Taking derivative of a function, which is defined implicitly</A> - <A HREF=https://www.algebra.com/algebra/homework/word/misc/Find-the-derivative-of-a-function-satisfying-given-functional-equation.lesson>Find the derivative for a function satisfying given functional equation</A> - <A HREF=https://www.algebra.com/algebra/homework/word/misc/A-tricky-Calculus-problem-on-derivative-and-anti-derivative.lesson>A tricky Calculus problem on derivative and anti-derivative</A> - <A HREF=https://www.algebra.com/algebra/homework/word/misc/Couple-of-non-standard-Calculus-problems.lesson#google_vignette>Couple of non-standard Calculus problems</A> - <A HREF=https://www.algebra.com/algebra/homework/word/misc/Finding-the-minimum-of-a-function-defined-on-a-curve-in-the-coordinate-plane.lesson>Finding the minimum of a function defined on a curve in a coordinate plane</A> - <A HREF=https://www.algebra.com/algebra/homework/word/misc/Tricky-solution-to-find-the-maximum-of-a-function-defined-by-a-complicated-expression.lesson>Tricky solution to find the maximum of a function defined by a complicated expression</A> - <A HREF=https://www.algebra.com/algebra/homework/word/misc/Maximize-the-area-of-a-trapezoid.lesson>Maximize the area of a trapezoid </A> - <A HREF=https://www.algebra.com/algebra/homework/word/misc/Maximmize-the-volume-of-an-open-box.lesson>Maximize the volume of an open box</A> - <A HREF=https://www.algebra.com/algebra/homework/word/misc/Minimize-surface-area-of-a-rectangular-prizm-with-the-given-volume.lesson>Minimize surface area of a rectangular box with the given volume</A> - <A HREF=https://www.algebra.com/algebra/homework/word/misc/Minimize-the-cost-of-an-aquarium-with-the-given-volume.lesson>Minimize the cost of an aquarium with the given volume</A> - <A HREF=https://www.algebra.com/algebra/homework/word/misc/Minimize-surface-area-of-a-conic-paper-cup-with-the-given-volume.lesson>Minimize surface area of a conical paper cup with the given volume</A> - <A HREF=https://www.algebra.com/algebra/homework/word/misc/Find-the-volume-of-a-solid-body-obtained-by-rotation-the-area-about-an-axis.lesson>Find the volume of a solid obtained by rotation of some plane shape about an axis</A> - <A HREF=https://www.algebra.com/algebra/homework/word/misc/Finding-the-volume-of-a-solid-body-mentally.lesson>Finding the volume of a solid body mentally</A> - <A HREF=https://www.algebra.com/algebra/homework/word/misc/OVERVIEW-of-my-lessons-on-Calculus-word-problems.lesson>OVERVIEW of my lessons on Calculus word problems</A> Use this file/link <A HREF=https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-II - YOUR ONLINE TEXTBOOK</A> to navigate over all topics and lessons of the online textbook ALGEBRA-II.
