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g

Domain: x > 5 , range: all real numbers

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g f

Domain: x > 2 and x < 4 , range: all real numbers

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Find the degree, y -intercept, and zeros for the following polynomial functions.

f ( x ) = 2 x 2 + 9 x 5

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f ( x ) = x 3 + 2 x 2 2 x

Degree of 3, y -intercept: 0, zeros: 0, 3 1 , −1 3

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Simplify the following trigonometric expressions.

tan 2 x sec 2 x + cos 2 x

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cos ( 2 x ) = sin 2 x

cos ( 2 x ) or 1 2 ( cos ( 2 x ) + 1 )

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Solve the following trigonometric equations on the interval θ = [ −2 π , 2 π ] exactly.

sec 2 x 2 sec x + 1 = 0

0 , ± 2 π

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Solve the following logarithmic equations.

Are the following functions one-to-one over their domain of existence? Does the function have an inverse? If so, find the inverse f −1 ( x ) of the function. Justify your answer.

f ( x ) = 1 x

One-to-one; yes, the function has an inverse; inverse: f −1 ( x ) = 1 y

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For the following problems, determine the largest domain on which the function is one-to-one and find the inverse on that domain.

f ( x ) = x 2 + 3 x + 4

x 3 2 , f −1 ( x ) = 3 2 + 1 2 4 y 7

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A car is racing along a circular track with diameter of 1 mi. A trainer standing in the center of the circle marks his progress every 5 sec. After 5 sec, the trainer has to turn 55° to keep up with the car. How fast is the car traveling?

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For the following problems, consider a restaurant owner who wants to sell T-shirts advertising his brand. He recalls that there is a fixed cost and variable cost, although he does not remember the values. He does know that the T-shirt printing company charges $440 for 20 shirts and $1000 for 100 shirts.

a. Find the equation C = f ( x ) that describes the total cost as a function of number of shirts and b. determine how many shirts he must sell to break even if he sells the shirts for $10 each.

a. C ( x ) = 300 + 7 x b. 100 shirts

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a. Find the inverse function x = f −1 ( C ) and describe the meaning of this function. b. Determine how many shirts the owner can buy if he has $8000 to spend.

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For the following problems, consider the population of Ocean City, New Jersey, which is cyclical by season.

The population can be modeled by P ( t ) = 82.5 67.5 cos [ ( π / 6 ) t ] , where t is time in months ( t = 0 represents January 1) and P is population (in thousands). During a year, in what intervals is the population less than 20,000? During what intervals is the population more than 140,000?

The population is less than 20,000 from December 8 through January 23 and more than 140,000 from May 29 through August 2

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In reality, the overall population is most likely increasing or decreasing throughout each year. Let’s reformulate the model as P ( t ) = 82.5 67.5 cos [ ( π / 6 ) t ] + t , where t is time in months ( t = 0 represents January 1) and P is population (in thousands). When is the first time the population reaches 200,000?

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For the following problems, consider radioactive dating. A human skeleton is found in an archeological dig. Carbon dating is implemented to determine how old the skeleton is by using the equation y = e r t , where y is the percentage of radiocarbon still present in the material, t is the number of years passed, and r = −0.0001210 is the decay rate of radiocarbon.

If the skeleton is expected to be 2000 years old, what percentage of radiocarbon should be present?

78.51%

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Find the inverse of the carbon-dating equation. What does it mean? If there is 25% radiocarbon, how old is the skeleton?

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Questions & Answers

A Function F(X)=Sinx+cosx is odd or even?
WIZARD Reply
neither
David
Neither
Lovuyiso
f(x)=1/1+x^2 |=[-3,1]
Yuliana Reply
apa itu?
fauzi
determine the area of the region enclosed by x²+y=1,2x-y+4=0
Gerald Reply
Hi
MP
Hi too
Vic
hello please anyone with calculus PDF should share
Adegoke
Which kind of pdf do you want bro?
Aftab
hi
Abdul
can I get calculus in pdf
Abdul
How to use it to slove fraction
Tricia Reply
Hello please can someone tell me the meaning of this group all about, yes I know is calculus group but yet nothing is showing up
Shodipo
You have downloaded the aplication Calculus Volume 1, tackling about lessons for (mostly) college freshmen, Calculus 1: Differential, and this group I think aims to let concerns and questions from students who want to clarify something about the subject. Well, this is what I guess so.
Jean
Im not in college but this will still help
nothing
how can we scatch a parabola graph
Dever Reply
Ok
Endalkachew
how can I solve differentiation?
Sir Reply
with the help of different formulas and Rules. we use formulas according to given condition or according to questions
CALCULUS
For example any questions...
CALCULUS
v=(x,y) وu=(x,y ) ∂u/∂x* ∂x/∂u +∂v/∂x*∂x/∂v=1
what is the procedures in solving number 1?
Vier Reply
review of funtion role?
Md Reply
for the function f(x)={x^2-7x+104 x<=7 7x+55 x>7' does limx7 f(x) exist?
find dy÷dx (y^2+2 sec)^2=4(x+1)^2
Rana Reply
Integral of e^x/(1+e^2x)tan^-1 (e^x)
naveen Reply
why might we use the shell method instead of slicing
Madni Reply
fg[[(45)]]²+45⅓x²=100
albert Reply
find the values of c such that the graph of f(x)=x^4+2x^3+cx^2+2x+2
Ramya Reply
anyone to explain some basic in calculus
Adegoke Reply
I can
Debdoot
Practice Key Terms 7

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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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