Math Answers

Q. Find the vectors t, n, b at the given point to the curve.
γ(t)=(t^2,2/3 t^3,t), (1, 2/3, 1)

Q. Reparameterize the curve w.r.t arc length parameter s.
γ(t)=(2t,1-3t,5+4t)

Q. Find the arc length of the curve
γ(t)=(t,lnt,tlnt), 1≤t≤2

A box contains 4 red and 5 blue marbles. Michele picks three marbles at random from this box. If Z is a random variable representing the # of blue marbles picked from the box, do the following:
a. Express the probability mass function of Z in tabular form.
b. Draw the corresponding histogram.
c. Compute the probability that Michele can pick more red marbles than blue from the box.

Find the antiderivative of the following:

1. ((3x^2+14x+13)/(x+4) dx
2. ((2x+5)/(3x-1) dx
3. ((x^5-2x^3-2x)/(x^2+1) dx
4. ((x^3+4x)/(x^2-1) dx

Find the antiderivative of (1+e^x)/(1-e^x) dx

Q. State and prove Hahn Banach theorem.

Q. State and prove Zorn, s Lemma.

A ship leaves a port P and sails for 12km on a bearing 068. it then sails a further 20km on bearing of 106 to reach Q. what is the distance between P & Q. what is the bearing of Q from P.

Suppose that airplane engines operate independently
and fail with probability equal to 0.4. Assuming
that a plane makes a safe flight if at least one-half of its
engines run, determine whether a 4-engine plane or a 2-
engine plane has the higher probability for a successful
flight.