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Suppose that A,B and C are sets such that A is the improper subset of B and B is the improper subset of C
6.12 The average length of steel nails is 5 centime ters, with a standard deviation of 0.05 centimeters. Assuming that the lengths are normally distributed, what percentage of the nails are
(b) between 4.95 and 5.05 centimeters in length?
(c) shorter than 4.90 centimeters?
(a) longer than 5.05 centimeters?
Use Cauchy’s Integral formulas to evaluate the following integral along the
indicated closed contours.
∮
z
2+3z+2i
z
2+3z−4
dz;
C
(a) |z| = 2 (b) |z + 5| =
3
2
Suppose z0 is any constant complex number interior to any simple closed
contour C. Show that for a positive integer n,
∮
dz
(z−z0)
n = {
2πi, n = 1
C 0, n > 1.
Use the truth tables method to determine whether (¬p ∨ q) ∧ (q → ¬r ∧ ¬p) ∧ (p ∧ r) is
satisfiable.
Are the statement true or false?give reason for your answers: the function,f(x) =sin^2x is uniformly continuous in the interval [0,π]
Are the statement true or false?give reason for your answers: the function f defined on r by f(x) ={0 x is rational 2 is irrational} Is integrable in the interval [2,3]
11. Find 8th term of the sequence 1,5,9.......
12. If central angle of an arc is 200º,then find the angle made by the arc on the
alternate arc?
13. Prove that a rectangle is always cyclic
14. If algebraic form of an arithmetic sequence is 3-5n,find first term and common
difference
15. Find number of multiples of 11 in between 100 a nd 200
(P^Q^R)V (¬P^Q^R)V(¬P^¬Q^¬R)
P2-xp-q=0 solve by charpit method
