College Algebra 1st Edition
ISBN: 9781938168383
Author: Jay Abramson
Publisher: Jay Abramson
1 Prerequisites 2 Equations And Inequalities 3 Functions 4 Linear Functions 5 Polynomial And Rational Functions 6 Exponential And Logarithmic Functions 7 Systems Of Equations And Inequalities 8 Analytic Geometry 9 Sequences, Probability And Counting Theory Chapter5: Polynomial And Rational Functions
5.1 Quardratic Functions 5.2 Power Functions And Polynomial Functions 5.3 Graphs Of Polynomial Functions 5.4 Dividing Polynomials 5.5 Zeros Of Polynomial Functions 5.6 Rational Functions 5.7 Inverses And Radical Functions 5.8 Modeling Using Variation Chapter Questions Section: Chapter Questions
Problem 1RE: For the following exercises, write the quadratic function in standard form. Then, give the vertex... Problem 2RE: For the following exercises, write the quadratic function in standard form. Then, give the vertex... Problem 3RE: For the following problems, find the equation of the quadratic function using the given information.... Problem 4RE: For the following problems, find the equation of the quadratic function using the given information.... Problem 5RE: For the following exercises, complete the task. 5. A rectangular plot of land is to be enclosed... Problem 6RE: For the following exercises, complete the task. An object projected from the ground at a 45 degree... Problem 7RE: For the following exercises, determine if the function is a polynomial function and, if so, give the... Problem 8RE: For the following exercises, determine if the function is a polynomial function and, if so, give the... Problem 9RE: For the following exercises, determine if the function is a polynomial function and, if so, give the... Problem 10RE: For the following exercises, determine end behavior of the polynomial function. f(x)=2x4+3x35x2+7 Problem 11RE: For the following exercises, determine end behavior of the polynomial function. f(x)=4x36x2+2 Problem 12RE: For the following exercises, determine end behavior of the polynomial function. f(x)=2x2(1+3xx2) Problem 13RE: For the following exercises, find all zeros of the polynomial function, noting multiplicities. 13.... Problem 14RE: For the following exercises, find all zeros of the polynomial function, noting multiplicities. 14.... Problem 15RE: For the following exercises, find all zeros of the polynomial function, noting multiplicities. 15.... Problem 16RE: For the following exercises, based on the given graph, determine the zeros of the function and note... Problem 17RE: For the following exercises, based on the given graph, determine the zeros of the function and note... Problem 18RE: For the following exercises. based on the given graph, determine the zeros of the function and note... Problem 19RE: For the following exercises, use long division to find the quotient and remainder. 19. x32x2+4x+4x2 Problem 20RE: For the following exercises, use long division to find the quotient and remainder. 20.... Problem 21RE: For the following exercises, use synthetic division to find the quotient. If the divisor is a... Problem 22RE: For the following exercises, use synthetic division to find the quotient. If the divisor is a... Problem 23RE: For the following exercises, use synthetic division to find the quotient. If the divisor is a... Problem 24RE: For the following exercises, use synthetic division to find the quotient. if the divisor is a... Problem 25RE: For the following exercises, use the Rational Zero Theorem to help you solve the polynomial... Problem 26RE: For the following exercises, use the Rational Zero Theorem to help you solve the polynomialequation.... Problem 27RE: For the following exercises, use the Rational Zero Theorem to help you solve the polynomial... Problem 28RE: For the following exercises, use the Rational Zero Theorem to help you solve the polynomial... Problem 29RE: For the following exercises, use Descartes’ Rule of Signs to find the possible number of positive... Problem 30RE: For the following exercises, use Descartes’ Rule of Signs to find the possible number of positive... Problem 31RE: For the following exercises. find the intercepts and the vertical and horizontal asymptotes, and... Problem 32RE: For the following exercises. find the intercepts and the vertical and horizontal asymptotes, and... Problem 33RE: For the following exercises, find the intercepts and the vertical and horizontal asymptotes, and... Problem 34RE: For the following exercises. find the intercepts and the vertical and horizontal asymptotes, and... Problem 35RE: For the following exercises, find the slant asymptote. f(x)=x21x+2 Problem 36RE: For the following exercises, find the slant asymptote. f(x)=2x3x2+4x2+1 Problem 37RE: For the following exercises, find the inverse of the function with the domain given. 37.... Problem 38RE: For the following exercises, find the inverse of the function with the domain given. 38.... Problem 39RE: For the following exercises, find the inverse of the function with the domain given. 39.... Problem 40RE: For the following exercises, find the inverse of the function with the domain given. 40. f(x)=2x33 Problem 41RE: For the following exercises, find the inverse of the function with the domain given. 41. f(x)=4x+53 Problem 42RE: For the following exercises, find the inverse of the function with the domain given. 42. f(x)=x32x+1 Problem 43RE: For the following exercises, find the unknown value. 43. y varies directly as the square of x. If... Problem 44RE: For the following exercises, find the unknown value. 44. y varies inversely as the square root ofx.... Problem 45RE: For the following exercises, find the unknown value. 45. y varies jointly as the cube of x and as z.... Problem 46RE: For the following exercises, find the unknown value. 46. y varies jointly as x and the square ofz... Problem 47RE: For the following exercises, solve the application problem. 47. The weight of an object above the... Problem 48RE: For the following exercises, solve the application problem. 48.The volume V of an ideal gas varies... Problem 1PT: Give the degree and leading coefficient of the following polynomial function. f(x)=x3(36x22x2) Problem 2PT: Determine the and behavior of the polynomial function. f(x)=8x33x2+2x4 Problem 3PT: Determine the and behavior of the polynomial function. f(x)=2x2(43x5x2) Problem 4PT: Write the quadratic function in standard form. Determine the vertex and axes intercepts and graph... Problem 5PT: Given information about the graph of a quadratic function, find its equation. Vertex (2,0) and point... Problem 6PT: Solve the following application problem. A rectangular field is to be enclosed by fencing. In... Problem 7PT: Find all zeros of the following polynomial functions, noting multiplicities. f(x)=(x3)3(3x1)(x1)2 Problem 8PT: Find all zeros of the following polynomial functions, noting multiplicities. f(x)=2x612x5+18x4 Problem 9PT: Based on the graph, determine the zeros of the function and multiplicities. Problem 10PT: Use long division to find the quotient. 2x3+3x4x+2 Problem 11PT: Use synthetic division to find the quotient. If the divisor is a factor, write the factored form.... Problem 12PT: Use synthetic division to find the quotient. If the divisor is a factor, write the factored form.... Problem 13PT: Use the Rational Zero Theorem to help you find the zeros of the polynomial functions.... Problem 14PT: Use the Rational Zero Theorem to help you find the zeros of the polynomial functions. 14.... Problem 15PT: Use the Rational Zero Theorem to help you find the zeros of the polynomial functions.... Problem 16PT: Use the Rational Zero Theorem to help you find the zeros of the polynomial functions.... Problem 17PT: Given the following information about a polynomial function, find the function. It has a double zero... Problem 18PT: Given the following information about a polynomial function, find the function. It has a zero of... Problem 19PT: Use Descartes’ Rule of Signs to determine the possible number of positive and negative solutions.... Problem 20PT: For the following rational functions, find the intercepts and horizontal and vertical asymptotes,... Problem 21PT: For the following rational functions, find the intercepts and horizontal and vertical asymptotes,... Problem 22PT: Find the slant asymptote of the rational function. f(x)=x2+3x3x1 Problem 23PT: Find the inverse of the function. f(x)=x2+4 Problem 24PT: Find the inverse of the function. f(x)=3x34 Problem 25PT: Find the inverse of the function. f(x)=2x+33x1 Problem 26PT: Find the unknown value. y varies inversely as the square of x and when x=3,y=2. Find y if x=1. Problem 27PT: Find the unknown value. 27. y varies jointly with x and the cube root of 2. If when x=2 and... Problem 28PT: Solve the following application problem. The distance a body falls varies directly as the square of... Problem 27PT: Find the unknown value. 27. y varies jointly with x and the cube root of 2. If when x=2 and...
Related questions
Solve for ((1 integral 0) x3 (2+2x4 )5 dx) instead
Transcribed Image Text: Evaluate the definite integral.
Step 1
If we let u= 2 + 2x4, then du = 8x
dx.
Step 2
If u = 2+ 2x is substituted into
(2 + 2x dx. then we have
2+ 2+9* dx = / u
uPx dx.
We must also convert x dx into an expression involving u.
Using du = &x° dx, then we get
du
x dx =
8
up-
Step 3
Thus the indefinite integral
x* (2 + 2x*)> dx
becomes
u du-
We must also convert the integral limits.
If x = 1, then u=
If x = 0, then u= 2
Step 4
Using u = 2+ 2x, then the integral / (2+ 2x) dx becomes
u du
This evaluates as
1 64
4
64
4 J2
15
15
2
-l00
With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.
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