MATH M25A - Moorpark College
... Evaluate the limit of a function using numerical and algebraic techniques, the properties of limits, and analysis techniques. Evaluate one-sided and two-sided limits for algebraic and trigonometric functions. Determine analytically whether a limit fails to exist. Determine whether a function is cont ...
... Evaluate the limit of a function using numerical and algebraic techniques, the properties of limits, and analysis techniques. Evaluate one-sided and two-sided limits for algebraic and trigonometric functions. Determine analytically whether a limit fails to exist. Determine whether a function is cont ...
`A` List Problems
... follows: If x is in the Cantor set and x = (.d1 d2 d3 d4 · · ·)3 where each dj is either 0 or 2, then define ϕ(x) = (.b1 b2 b3 b4 · · ·)2 where bj = dj /2. If x is not in the Cantor set, let ϕ(x) = ϕ(x` ). (f) Using your answer to part (b) above, show that if x is not in the Cantor set, then ϕ(x) = ...
... follows: If x is in the Cantor set and x = (.d1 d2 d3 d4 · · ·)3 where each dj is either 0 or 2, then define ϕ(x) = (.b1 b2 b3 b4 · · ·)2 where bj = dj /2. If x is not in the Cantor set, let ϕ(x) = ϕ(x` ). (f) Using your answer to part (b) above, show that if x is not in the Cantor set, then ϕ(x) = ...
Limits, Sequences, and Hausdorff spaces.
... condition, called the Hausdorff condition, that ensures this pathological behavior does not occur. In the second part of the lecture we review the notion of continuity for function f : Rn → Rm in terms of open sets. This leads us to the definition of continuity for function f : X → Y between topolog ...
... condition, called the Hausdorff condition, that ensures this pathological behavior does not occur. In the second part of the lecture we review the notion of continuity for function f : Rn → Rm in terms of open sets. This leads us to the definition of continuity for function f : X → Y between topolog ...
Full text - The Fibonacci Quarterly
... for some « E { 1 , . . . , k}. E x a m p l e . Consider 9{x) = ( 3 * i ) . . . (3Yn)[(X + 1 .= Y?) A • • • A (X + n = Yn2)] so that 9(X) asserts that X - f l , X + 2 , . . . , X + n are perfect squares within the field. In this case one can take k = 2 with /xi = l / 2 n and / j 2 = 1. The first valu ...
... for some « E { 1 , . . . , k}. E x a m p l e . Consider 9{x) = ( 3 * i ) . . . (3Yn)[(X + 1 .= Y?) A • • • A (X + n = Yn2)] so that 9(X) asserts that X - f l , X + 2 , . . . , X + n are perfect squares within the field. In this case one can take k = 2 with /xi = l / 2 n and / j 2 = 1. The first valu ...
Here
... find points xi , yi arbitrarily close to a such that f (xi ) = f (yi ). But by Rolle’s Theorem this implies that there are points ci , between xi and yi , with f 0 (ci ) = 0. As xi and yi approach a, so does ci , so f 0 (a) = lim f 0 (ci ) = lim 0 = 0 (where we have used the fact that f 0 is continu ...
... find points xi , yi arbitrarily close to a such that f (xi ) = f (yi ). But by Rolle’s Theorem this implies that there are points ci , between xi and yi , with f 0 (ci ) = 0. As xi and yi approach a, so does ci , so f 0 (a) = lim f 0 (ci ) = lim 0 = 0 (where we have used the fact that f 0 is continu ...
Fibonacci Rectangles - Oldham Sixth Form College
... In mathematics, the Fibonacci numbers are a sequence of numbers named after Leonardo of Pisa, known as Fibonacci, whose Liber Abaci published in 1202 introduced the sequence to Western European mathematics. The sequence is defined by the following recurrence relation: ...
... In mathematics, the Fibonacci numbers are a sequence of numbers named after Leonardo of Pisa, known as Fibonacci, whose Liber Abaci published in 1202 introduced the sequence to Western European mathematics. The sequence is defined by the following recurrence relation: ...
Graph Sketcher Suggestions
... Choose the list of x values (-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5 might be a good list) and then calculate the corresponding y values. Use this chart to fill in the points to be plotted in simpleplot. To do the explorations below, be sure to calculate many points (10 or more). Exploration 1: Up and ...
... Choose the list of x values (-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5 might be a good list) and then calculate the corresponding y values. Use this chart to fill in the points to be plotted in simpleplot. To do the explorations below, be sure to calculate many points (10 or more). Exploration 1: Up and ...
