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1. Determine the largest domain Ω on which the function f(z) = log z / z is analytic, where log z is the principal branch of the logarithm. Furthermore, compute f'(z) on your domain Ω.
If u(x, y) = (1/2) ln(x2 + y2) and v(x, y) = tan-1 y/x, then is f(x + iy) = u(x, y) + iv(x, y) analytic on Ω, where Ω is the complex plane with the point z = 0 removed?
1. show using algebra that the formula for a circle is a special case of the formula for an ellipse.2. show using
How do you know if there are local extrema when there are no zeros after you take the derivative?
Mary's age now is 6 years more than twice the sum of the ages of her two children. In 3 years her age will be 22 years less than three times the sum of their ages. How old is Mary now?
The derivative of a continuous function at x is the slope of the tangent line to the curve at x. The attached pdf file develops the idea of a derivative first using slopes of secant lines and then introducing and explaining the difference quotient..
Griselda budgets 45 per month before sales tax for clothes. How much will she spend on clothes each month if she is charged 6 sales tax?
Find the minimum and maximum of P = 7x + 4y subject to
Make a table showing the probability distribution function(pdf) and cumulative distribution function (cdf) for X. Hint: draw a probability tree modeling the game.
Find the integrals- 1∫5 s ds / √(s2 + 4). Use the quotient rule to differentiate- y= (2x4 - 3x) / (4x - 1). Sketch the curve for y = sin(x) between x = 0 and x = 2Π.
Two point charges q1 and q2 separated by a distance of 3m experience a mutual force of 16x10^-15N. Calculate the magnitude of charge when q1=q2=q. What will be magnitude of force if separation between the charges is changed to 6m?
According to the empirical rule, almost all the data should lie between (x-3s) and (x+3s). The range accounts for all the data.
A college believes that 28% of applicants to that school have parents who have remarried. How large a sample is needed to estimate the true proportion of students who have parents who have remarried to within 6 percentage points with 95% confidenc..
b. Calculate the number of days with a demand for 3 days. Calculate the probability of two bottles per day
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