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Find the real part of the complex number a + bi obtained as the square root...
Find the area of the surface obtained by rotating the given curve about the x-axis. x = 20 cos (0), y = 20 sinº (0), 0 <O< 2 Preview
17. Fix a nonzero complex number Zo. Show that the set D obtained from the plane by deleting the ray {tz: 0<t< 0} is a domain.
Find the constant a such that the function is continuous on the entire real line. f(x) = [ 5x2, x 21 ax - 5, x < 1 a =
3i)16 in polar form: z r(cos 0isin 0) where (1 Write the complex number z and e= The angle should satisfy 0 0 < 2«.
If cos theta= square root 11/6 and tan theta < 0, find the exact value of sin the 1. If cos os (0) – VII and tan(Q) <o, find the exact value of sino).
We write R+ for the set of positive real numbers. For any positive real number e, we write (-6, 6) = {x a real number : -e < x <e}. Prove that the intersection of all such intervals is the set containing zero, n (-e, e) = {0} EER+
Find all complex variables z E C with Izl < 10 that satisfy e: +2e-:-3. 23
a) The root mean square displacement for diffusion in the x-direction is <x2> = 201 Use this result to show the rms displacement for diffusion in three dimensions is 6Dt. Hint: Use the Pythagoras equation.
For each complex number determine the angle, 0, from 0 <o<2n, and the length r. Round to three decimal places when necessary. y=-8 - 10i ry Oy
Express the real part of the following signal in the form Ae-at cos(wt + ?) where a, co and ? are real and-? < ? 2. ? b. x(t) = je(4+/100)t L or a nower signal. Then