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Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.2: Graphs Of Equations

Problem 78E

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Symmetric with respect to the X-axis
Symmetric with respect to the Y-axis
Symmetric with respect to the origin
None of these
Symmetric with respect to the X-axis
SymmetricC with respect to the Y-axis
*******
Symmetric with respect to the origin
None of these

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Working directly from definition, prove that if zn and wn are sequences of complex numbers withlimn→∞zn = 4 + 3i, and limn→∞wn = 4 − 3i,then limn→∞zn · wn = 25. (You may use the fact that convergent complex sequences are bounded.)
Picard's theorem states that in any arbitrarily small neighborhood of a singularity isolated essential z0 an analytic function f takes all finite complex values, with one exception, an infinite number of times. Since z = 0 for is an essential isolated singularity of f(z)= e^(1/z); find an infinite number of z in any neighborhood of z = 0 for which f(z) = i. Which is the only exception?. That is, what is the only value that does not take f(z)= e^(1/z)?
Fast solution Prove that the only idempotent elements in an integral domain R with unity are 0 and 1.
1) show that a GP has a limiting sum if 0<1-r < 2 2) by calculating the common ratio show that there is no GP with 1st term 8 and limiting sum 2. 3) a GP has positive 1st term a and has a limiting sum Sinfinite , show that Sinfinite > (1/2 )a. 4) fjind the reange of values of the limiting sum of a GP with i) a = 6 , ii) a = -8, iii) a>0 iv) a<0
1.What is the difference between rational and irrational numbers in their decimal representation?2. Give an example of a fraction p/q whose decimal expansion ends.3. Give an example of a fraction p/q whose decimal expansion repeats but does not end.4.What fraction, in form p/q, is represented by the decimal 0.12121212...?5.The xy-plane can represent a 2-dimensional, static region in space. What new perspective allows the xy-plane to represent a changing, dynamic world?6.If you don't like fractions and find the irrational numbers just too mysterious, what mathematician would you be drawn to?
Working directly from the definitions (and without using theCauchy Completeness Theorem) show that any Cauchy sequence of complexnumbers is bounded.
Absolute value of a conjugate Show that | z | = | z |.
Proof Prove properties 2, 3, and 4 of Theorem 2.6.

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