I know a is removable, but need proof. B is discontinuous/infinite but need proof. C is infinite but need proof. They can be proved with definitions or with examples.
I know a is removable, but need proof. B is discontinuous/infinite but need proof. C is...
I need to know how to proof (b) part. I didn't understand the original answer. 3. (a) Write the sum 147+10 (6n -2) using sigma notation. Solution: 2n i=1 (b) Use Mathematical Induction to prove that for all n 2 1, the above expression is equal to n(6n-1
(O)(w) Give the size of each set and also whether it is discrete or continuous. If the set is infinite, determine if it is countably infinite or not. a. A = {seven-digit numbers} b. B = {r: 2x = 1} c. C = {3:0 <r<1 and 1/2 <r <2} d. D = {(x,y): x2 + y2 = 1} e. E = {2:02 + 3x + 2 = 0} f, F = {positive even integers }
Subject: Proof Writing (functions) In need of help on this proof problem, *Prove the Following:* Here are the definitions that we may need for this problem: 1) Let f: A B be given, Let S and T be subsets of A Show that f(S UT) = f(s) U f(T) Definition 1: A function f from set A to set B (denoted by f: A+B) is a set of ordered Pairs of the form (a,b) where a A and b B...
Hi, I really need help on both parts a and b of this Complex Analysis question. Thanks! 1. Define exp(iy) := cos(y) + i sin(y). a. Prove, using trigonometry, that exp(iy+iy') = exp(iy). expliy') for y, y' ER two real numbers. b. Prove directly (using Taylor series for sin and cos) that expliy) = " where n! denotes the factorial of n. Hint: you may use the fact that an infinite sum of complex numbers an converges if and only...
Can I know how to do part(c)? I know how to do (a)(b). By (a) and (b), I get this 4 results. 1. ▾.F = 2xz5-2xz+3xz2 2. ▾xF = (2xy) i + (5x2z4-z3) j -(2yz) k 3. ▾.(▾xF) = 0 4. ▾x(▾f) = 0 Next, i need to calculate part (c). I want the solution of part(c), so don't give me the result of part(a) and (b) again, thanks! 1. (25 marks) (a) Evaluate . F and V. (V x...
need to fix. please have good handwriting 3). since we know that XXE A, X na sa therefore, if aina2 *a. E[az] XE[a] by symmetricity aa~a, A2E[a ] but also aie [a ] and az € [az] ~ Coy reflexivity So, [a. In = [az] iait (az] - and dit [a ] P 02] us lalu these needs to be proved. You can't just [a.] u ç[az] - say them Problem 7.1 Let be an equivalence relation on a set...
We already know the functions defined by y =C+a•f[b(x-d)] with the assumption that b>0. To see what happens when b<0, work parts (a)-(f) in order. (a) Use an even-odd identity to write y = sin(-2x) as a function of 2x. y= (b) How is your answer to part (a) related to y = sin(2x)? O It is the negative of y = sin (2x). olt equals y = sin (2x). (c) Use an even-odd identity to write y = cos(...
We already know the functions defined by y =c+a+f[b(x-d)] with the assumption that b>0. To see what happens when b<0, work parts (a)-(f) in order. (a) Use an even-odd identity to write y = sin (-2x) as a function of 2x. y = (b) How is your answer to part (a) related to y = sin (2x)? O It is the negative of y=sin (2x). It equals y=sin (2x). (c) Use an even-odd identity to write y = cos(-5x) as...
I need help completing the WHOLE problem, parts A, B, C, and D. I know it is a long problem, would appreciate labelled and clear steps, thank you. Kepler's Laws I. A planet revolves around the sun in an elliptical orbit with the sun at one focus. 2. The line joining the sun to a planet sweeps out equal areas in equal times. 3. The square of the period of revolution of a planet is proportional to the cube of...
i need help with all parts. i will rate. thank you very much. Let C be the closed curve consisting of two pieces. One piece is the upper-half circle of radius 3, centered at the origin, oriented counter-clockwise. The other piece is the horizontal line segment from (-3,0) to (3,0). Evaluate the line integral $ (x2 + y2)dx + (6xy—y?)dy = с (-3,0) (3,0) O 36 O 72 O 31 91/2 The level set of f(x,y) = 12 is a...