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Assume that (X, d) is a metric space and let (x1, : : : , xn) be a nite set of pointsof X. Elustrate , using only the de nition of open, that the set X\(x1, : : : , xn) obtained by removing every xi from X is open in X. (Sketch a picture to get some intuition!)
Find the number of square feet of pavement required for the shaded portion of the streets shown in the figure, all the streets being 50 feet wide.
-x^3+6x-7
Extrema : Note as well that while we say an "open interval around x = c " we mean that we can discover some interval ( a, b ) , not involving the endpoints, such that a Also,
Evaluate following integrals. (a) ∫ 3e x + 5 cos x -10 sec 2 x dx (b) ( 23/ (y 2 + 1) + 6 csc y cot y + 9/ y dy Solution (a) ∫ 3e x + 5 cos x -10 sec 2 x
Proper and Improper Fractions: Example: 3/8 proper fraction 8/3 improper fraction 3/3 improper fraction Here an improper fraction expressed as the sum of an in
a boy is six months old his sister was given birth to three month after him. if their cousin is 0.33years old, arrange their ages in ascending order
Let {An} be sequence of real numbers. Define a set S by: S={i ? N : for all j > i, ai
Determine if the following sequences are monotonic and/or bounded. (a) {-n 2 } ∞ n=0 (b) {( -1) n+1 } ∞ n=1 (c) {2/n 2 } ∞ n=5 Solution {-n 2 } ∞ n=0
The area of a rectangle is 24 square inches. The length of the rectangle is 2 inches more than the width. How many inches is the width? Let x = the number of inches in the widt
The Definition of the Derivative : In the previous section we saw that the calculation of the slope of a tangent line, the instantaneous rate of change of a function, and the ins
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