### Drawing graphs of straight lines , parabolas , hyperbolas and circles

Different equations are given on the attached paper and their graphs are to be drawn.

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Different equations are given on the attached paper and their graphs are to be drawn.

Important Formulas and their Explanations (II): Gradient, Divergence and Curl Gradient of the differnece of two scalar point functions.

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Function A Function B (n^2) ! n^n is A=O(B) ? Yes/No is A=o(B) ? Yes/No is A=Big Omega(B) ? Yes/No is A=Small Omega(B) ? Yes/No is A=Theta(b) ? Yes/No Thanks

Please see the attached file for the fully formatted problems. Includes: Solving equations, graphing equations, finding domains, simplyfing, determine the inverse of f using the switch and solve strategy. Thanks for your help!

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Plot your data for each disease as points in a rectangular coordinate system. Year...................1985..........1990..........1995......2002 Heart Disease 771,169 720,058 684,462 162,672 Cancer 461,563 505,322 554,643 557,271 AIDS * 8,000 25,188 39,979 14,095 - Use individu

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Consider the function u(x,t) = sin(4 pi x) e^(-pi t). Plot using a graphical tool and explain what you observe. Please see the attached file for the fully formatted problems.

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See attached

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Let a<b. Let f_n: [a,b] -> R be a sequence of functions such that, for each n in N ( N set of natural numbers),f_n is differentiable on (a,b). Suppose that for all n in N, Sup on [a,b] of | f'_n(x) | < or = to M, where M is in R. ( Sup is supremum = least upper bound) Prove that for all n in N and all x, y in [a,b], one has

Let f_n : [0,1] -> R be a sequence of continuous functions such that for each n in N (natural numbers), f_n is differentiable on (0,1). Suppose that f_n(0) converges to some number, denoted f(0), and also suppose that the sequence (f'_n) converges uniformly on (0,1) to some function g: (0,1) -> R. Prove that the sequence (f_n) c

3. Suppose that u(x. t) satisfies the diffusion equation ut = kuxx for 0 < x < L and t > 0, and the Robin boundary conditions ux(0, t) ? aou(0, t) = 0 and ux(L, t) + aLu(L, t) = 0 where k, L, a0 and aL are all positive constants. Show that ... is a decreasing function of t. Please see the attached file for the fully for

Given equation [3/(x+1)]+4, please find ... V.A.:__________ H.A.:__________ y-int:__________ X-int:__________ Graph:__________

Sketch the graph of the function y= -x^3+3x^2-4. Be sure to include and label: 1.) x and y intercepts 2.) asymptotes 3.) 1st and 2nd derivatives 4.) increasing and decreasing intervals 5.) intervals of concavity 6.) inflection point(s) 7.) relative extrema (max and min)

Identify the point of diminishing returns for the input-output functions. R=1/50000(600x^2-x^3), 0<x<400 (those are < or = to signs) R=-4/9(x^3-9x^2-27), 0<x<5 (those are < or = to signs)

A car travels along a straight road, heading West for 3 hours, and then travels NE on another road for 2 hours. If the car has maintained a constant speed of 55 mi/hr, how far is it from its starting point?

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Let F be a field and le p(x) E F[x]. If p(x) is not irreducible, then F[x]/{p(x)} is: a) always a field b) sometimes a field c) never a field. Give reasons for your assertion. Please see attached.