Complex Analysis Answers

Give the definition of Banach spaces and explain why this notion is important only when
working with infinite dimensional vector spaces.

Let {sn}, {tn} and {un} be sequences such that sn< tn <un for all n. Prove that if sn approaches L and un approaches L, then tn approaches L

Find the normalizer of each subgroup of D[sub]2[/sub]

Show that the line y = x + 2 is a tangent to the parabola y = x[sup]2[/sup]

(a) Show that the line y = x + 2 is a tangent to the parabola y = x[sup]2[/sup]- 5x + 11.
(b) Let Q be the point where these two functions intersect. Determine the equation of thenormal to the parabola at Q.
(c) Find the area of the region enclosed between the parabola and the normal to theparabola at Q.

A supertanker spilled a total of 198666 barrels of oil. How many liters would this be? Given 1 barrel = 42.0 gal; 1 gal = 4 quarts and 1 quart = 9.46x10-4 m3?

Assume that a,b are real numbers. Show a^2 +b^2=0 implies a=b=0