# fuction

1. ### finding critical points of a fuction

I first find the derivative of the function using the quotient rule, to get \frac{1-lnx}{x^2} and set equal to zero and solve to get x=e is this correct, or are there are there more steps?
2. ### determining the domain of a fuction

So Determine the domain of this fuction y=√x^2-16 so first i factorised and get (x+4) and (x-4) i m sure the domain has to be between -4 <x<4 what i am confused about is what happens to the square root , can some 1 how me how to do the proper workout for this problem ? cheers (Rofl)
3. ### composite of a fuction

Deﬁne the composite of a function f from X to Y and a function g from Y to Z.
4. ### Derivative of inverse tan fuction

I was having trouble with the following question about finding the derivative of: y=(tan^-1(x/2))^4 -i utilized the chain rule but this came out to be wrong.
5. ### Rotation around y and x axis + shifting the fuction

The first problem states to set up a formula for the volume which u get when the area limited by y=X²+1 and y=5 rotates around y=5. The second problem states to set up a formula for the volume when the area limited by X=2 and y=(8X)^(1/2 rotates around x=2. My progress on the first part is...
6. ### Modelling with exponential fuction.

The growth rate of a plant during the first week after germination is given by g(t)=ae^(t/2) mm/day, where the time t is measured in days, and a is a constant. a) Determine the height of the plant h(t) as a function of the time t, assuming that it was zero at time t=0. b)On the first day...
7. ### Inverse Laplace Transform of the following fuction

So the question is: Solve the initial value problem using the method of Laplace transforms: y'' + 2y' +10y = g(t) where g(t) = { 10, 0<=t<=10 { 20, 10<t<20 { 0, 20< t so i got it to Y(s) = now after this if someone can help me take the inverse laplace...
8. ### Prove continuity of a fuction

Prove that f(x)={xsin(1/x), if x≠0 { 0 , if x=0 is continuous using i) language of limits ii) ε - δ - language Please help me (Worried) Thanks in advance for any replies. Feyomi.
9. ### Gamma fuction and integral

Hello. I just cant solve this problem. Who can do it? Using gamma fuction calculate the following integral: \int_o^1 x^3 [ln(\frac{1}{x})]^3 dx Thanks a lot¡¡
10. ### Beta fuction

Hello. Who can help me to prove the following? B(p,q) = \displaystyle\frac{q-1}{p}B(p+1,q-1)= \displaystyle\frac{p-1}{q}B(p-1,q-1) p,q > 1 Thanks
11. ### inverse fuction help !

hi (Rock) im struggling with this question and was wondering if anyone can help this is the question... find the inverse the function is defined by f(x) = ln(4x-1) , x>1/4 all help is fully appriciated thank you
12. ### Finding the value of a Fuction

In 1999, the population of a country was estimated at 4 million. For any subsequent year the population P(t)=240/5+54.99e^-0.0208t where t is the number of years since 1999. estimate the population in 2016. help me please(Crying)
13. ### Prove about no bijective fuction exist

Let S={a,b,c,d,e} and let T be the set of all ten 2-element subsets of S. Show that there exists no injective function f:S→{0,1,2,...,|T|} such that the function g: T→ {1,2,...,|T|} defined by g({i,j})=|f(i)-f(j)|is bijective.
14. ### Differentiate fuction

Differentiate the following function. y ' = ? ATTEMPT y=x^1/2(5x-2) = 5x^(3/2)-2x(1/2) = (15/2)x^(1/2)-x^(-1/2) Then from this step I am lost. So please help me out! THANKS! (Rofl)
15. ### Limit represent the derivative of some fuction.

At first I thought that it is (a) but then i realized that even if it's derivative it is possible that it wont turn out to be cos. If I am correct this time, the answer should be (c) f(x)=sin(x), a= pie/4 (Rofl)(Rofl)(Rofl) am i correct? :) thank you!!!
16. ### Determining if Y is a Fuction of X in an Equation

How can one determine without graphing if an equation represents y as a function of x. For example what would make {16x^2-y^2=0} not a function? And yet {y=sqrt(1-x)} a function. How is this determined? Are there varieties of ways of determining weather an equation is a function depending what...