Calculus Answers

A dam is overflowing at the rate of
V ′(t) = 6t(2t + 1)−2 thousand m3 per day,
where t is the time in days after the overflow begins. Find the amount of water that overflows from the dam during the second day of the overflow. Give the answer exactly first and then to 4 significant figures.

step by step working out

Let f(x) = 8+(2x+3)ln(√x+x−1)
(a) Find the derivative of f.
(b) Using the derivative, estimate f(1.1).

need step by step working out

The diameter of a cat's pupil is given by f(x) = (160x^-0.4 + 90)/(4x^-0.4+15) where x is the intensity of light on the pupils.
1. By considering lim as x tends to infinity of f(x), determine the diameter of the cat's pupils due to very intense light.
2. Show that f(x) may be written as f(x)=(160+90x^0.4)/(4+15^0.4)
3. Deduce the diameter of the cat's pupil for as light diminishes to a minimum intensity.

Show that the equation x5+y5-16 x3 y -1=0 determines a solution fi around the point x=1 such that fi(1)=2 . Find the first derivative of the solution and its value at (1,2) .

W(t) = 1.5 ln ((t/4)+1) where t ≥ 0 and W(t) is the mean weight of a lobster in kg after t months.
a) draw this function so as to depict the mean weight of a lobster over 2 years of its growth
b) Graphically determine the time taken, in months, for the mean weight of a lobster to reach 2.56kg. Check the answer using an algebraic approach

Hi sam here i need some help...
what is the hypotenuse.
of question 5 in the book.

Determine whether each of the following converges or diverges:
∞
1) ∑ 1/n^2+1
n-1

∞
2) ∑ 2^n+5/3^n
n-0

∞
3) ∑ sin k/k^2
k-1

Find the domain of the function f and evaluate f(3,2).
(x,y)=x ln(y2-x) .

Evaluate the limit :
lim x tends to infinite {(sin(1/x))/(e(1/x)-1)} .

The function f defined by f(x,y,z)=x2+2y+z is integrable on [0,2]*[2,4]*[4,6] .