




Card 20 / 28:
increasing on the interval I
a function increasing on the interval I if for all x 1 , x 2 ∈ I , f ( x 1 ) ≤ f ( x 2 ) if x 1 < x 2

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Questions & Answers
an expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable(s).
Alif
a term/algebraic expression raised to a nonnegative integer power and a multiple of coefficient,,,,,, T^n where n is a nonnegative,,,,, 4x^2
joe
what is hyperbolic function
find volume of solid about y axis and y=x^3, x=0,y=1
how do i deal with infinity in limits?
Add the functions f(x)=7xx g(x)=5x
difference btwn domain co domain and range
Cabdalla
The set of inputs of a function. x goes in the function, y comes out.
Verna
If you differentiate then answer is not x
Raymond
domain is the set of values of independent variable and the range is the corresponding set of values of dependent variable
Champro
give different types of functions.
Paul
how would u find slope of tangent line to its inverse function, if the equation is x^5+3x^34x8 at the point(8,1)
pls solve it i Want to see the answer
Sodiq
differentiate each term
Friendz
why do we need to study functions?
to understand how to model one variable as a direct relationship to another variable
Andrew
integrate the root of 1+x²
use the substitution t=1+x.
dt=dx
√(1+x)dx = √tdt
= t^1/2 dt
integral is then
= t^(1/2 + 1) / (1/2 + 1) + C
= (2/3) t^(3/2) + C
substitute back t=1+x
= (2/3) (1+x)^(3/2) + C
navin
find the nth differential coefficient of cosx.cos2x.cos3x
determine the inverse(onetoone function) of f(x)=x(cube)+4 and draw the graph if the function and its inverse
f(x) = x^3 + 4, to find inverse switch x and you and isolate y:
x = y^3 + 4
x 4 = y^3
(x4)^1/3 = y = f^1(x)
Andrew
in the example exercise how does it go from
4 + squareroot(8)/4
to
4 + 2squareroot(2)/4
what is the process of pulling out the factor like that?
can you please post the question again here so I can see what your talking about
Andrew
√(8)
=√(4x2)
=√4 x √2
2 √2
hope this helps.
from the surds theory
a^c x b^c = (ab)^c
Barnabas
can you determine whether f(x)=x(cube) +4 is a one to one function
Crystal
one to one means that every input has a single output, and not multiple outputs. whenever the highest power of a given polynomial is odd then that function is said to be odd. a big help to help you understand this concept would be to graph the function and see visually what's going on.
Andrew
one to one means that every input has a single output, and not multiple outputs. whenever the highest power of a given polynomial is odd then that function is said to be odd. a big help to help you understand this concept would be to graph the function and see visually what's going on.
Andrew
can you show the steps from going from
3/(x2)= y
to
x= 3/y +2
I'm confused as to how y ends up as the divisor
step 1: take reciprocal of both sides
(x2)/3 = 1/y
step 2: multiply both sides by 3
x2 = 3/y
step 3: add 2 to both sides
x = 3/y + 2
ps nice farcry 3 background!
Andrew
first you cross multiply and get y(x2)=3
then apply distribution and the left side of the equation such as yx2y=3
then you add 2y in both sides of the equation and get yx=3+2y
and last divide both sides of the equation by y and you get x=3/y+2
Ioana
Multiply both sides by (x2) to get 3=y(x2)
Then you can divide both sides by y (it's just a multiplied term now) to get 3/y = (x2). Since the parentheses aren't doing anything for the right side, you can drop them, and add the 2 to both sides to get 3/y + 2 = x
Melin
thank you ladies and gentlemen I appreciate the help!
Robert
keep practicing and asking questions, practice makes perfect! and be aware that are often different paths to the same answer, so the more you familiarize yourself with these multiple different approaches, the less confused you'll be.
Andrew
Source:
OpenStax, Calculus volume 1. OpenStax CNX. Feb 05, 2016 Download for free at http://cnx.org/content/col11964/1.2
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