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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

find the integral of tan
Gagan Reply
Differentiate each from the first principle. y=x,y=1/x
Abubakar Reply
I need help with calculus. Anyone help me.
Macquitasha Reply
yes
Pradip
formula for radius of curvature
mpradeepa Reply
Hi
Usman
beautiful name usman
Fund
really
Usman
Hi guys
Macquitasha
Hello everyone here
abdulazeez
good day!
joel
hii
Shreya
You are welcome
abdulazeez
shreya
ashif
thanks
joel
hello Sar aapse Kuchh calculate ke sawal poochhne Hain
Sumit
integration seems interesting
Fund Reply
it's like a multiple oparation in just one.
Efrain
Definitely integration
ROHIT Reply
tangent line at a point/range on a function f(x) making f'(x)
Luis
Principles of definite integration?
ROHIT
For tangent they'll usually give an x='s value. In that case, solve for y, keep the ordered pair. then find f(x) prime. plug the given x value into the prime and the solution is the slope of the tangent line. Plug the ordered pair into the derived function in y=mx+b format as x and y to solve for B
Anastasia
parcing an area trough a function f(x)
Efrain
Find the length of the arc y = x^2 over 3 when x = 0 and x = 2.
Jade Reply
integrate x ln dx from 1 to e
Sourav Reply
application of function
azam Reply
how i can need help
azam Reply
what ?
Bunyim
defination of math
azam
application of function
azam
please reply fast
azam
what is a circle
Ronnie
math is the science, logic, shape and arrangement
Boadi
a circle is a hole shape
Jianna
a whole circumference have equal distance from one point
azam
please tell me books which write on function
azam
HE is a Nigerian, wrote the book INTEGRATED MATHEMATICS...CHECK IT OUT!!
Agboke
Woah this is working again
Bruce
show that the f^n f(x)=|x-1| is not differentiable at x=1.
Mohit Reply
is there any solution manual to calculuse 1 for Gilbert Strang ?
Eng Reply
I am beginner
Abdul
I am a beginner
ephraim
l am also beginner
Badar
just began, bois!!
Luis
Hello
abdulazeez
I am newer
abdulazeez
Hey
Bonface
Hi
Jianna
what is mathematics
Henry Reply
logical usage of numbers
Leo
thanks
Henry
you welcome
Leo
what's career can one specialize in by doing pure maths
Lucy
Lucy Omollo...... The World is Yours by specializing in pure math. Analytics, Financial engineering ,programming, education, combinatorial mathematics, Game Theory. your skill-set will be like water a necessary element of survival.
David
***onetonline.org/find/descriptor/result/1.A.1.c.1
Bruce
mathematics seems to be anthropocentric deductive reasoning and a little high order logic. I only say this because I can only find two things going on which is infinitely smaller than 0 and anything over 1
David
More comprehensive list here: ***onetonline.org/find/descriptor/result/1.A.1.c.1?a=1
Bruce
so how can we differentiate inductive reasoning and deductive reasoning
Henry
thanks very much Mr David
Henry
hi everyone
Sabir
is there anyone who can guide me in learning the mathematics easily
Sabir
Hi Sabir first step of learning mathematics is by falling in love with it and secondly, watch videos on simple algebra then read and solved problems on it
Leo
yes sabir just do every time practice that is the solution
Henry
it will be work over to you ,u know how mind work ,it prossed the information easily when u are practising regularly
Henry
in calculas,does a self inverse function exist
Lucy
I'm lost in all functions need help
Jonathan
hello i need help in rate of change
Moises
***questioncove.com/invite/QzOQGp
Bruce
Hello
hassan
hi
MJ
hi
Masaniel
so difficult
Masaniel
hello my name is Charles Christian
Charles Reply
Hello Charles
Jianna
Hi! I am Dante
Dante
Hi! I'm ashwini
ashwini
halĺo
Roben
Hi
Leo
hello leo
Agboke
can anyone prove why AU(BnC)=(AUB)n(AUC)
Agboke
this one it can't be proven these are assumption
Henry
hello agboke there is no proof for such
Leo
Hi
Adewale
hi this is wasim
wasim
can anybody put me through flowchart and algorithm here
Agboke
download introductory books and read
Leo
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Luis
music while you math
Luis
dy/dx= 1-cos4x/sin4x
Alma Reply
what is the derivatives of 1-cos4x/sin4x
Alma
what is the derivate of Sec2x
Johar
d/dx(sec(2 x)) = 2 tan(2 x) sec(2 x)
AYAN
who knows more about mathematical induction?
Agboke
who know anything about the whole calculus thing 🤔 its killing me 😶
matbakh
Yes
Dadi
hii
Gagan
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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