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17 марта 2021 г. 8:00:48
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Find the exact length of the polar curve r = e^(2 theta) over [0, 2 pi].Find the exact length of the polar curve r = e^(2 theta) over [0, 2 pi].Find equation of tangent line to graph y = x^2 at (2, 4). GraphFind equation of tangent line to graph y = x^2 at (2, 4). GraphFind the sum of the series {1- ln 2 + (ln 2)^2/2! - (ln 2)^3/3! + …}. Use Maclaurin series tableFind the sum of the series {1- ln 2 + (ln 2)^2/2! - (ln 2)^3/3! + …}. Use Maclaurin series tableFind solution of differential equation dy/dx that satisfies initial condition y(0) = -3Find solution of differential equation dy/dx that satisfies initial condition y(0) = -3Find polar equation of curve that is represented by Cartesian equation 4y^2 =xFind polar equation of curve that is represented by Cartesian equation 4y^2 =xDraw 3 cards from 52 card deck. Find probability of drawing exactly 2 red cards without replacementDraw 3 cards from 52 card deck. Find probability of drawing exactly 2 red cards without replacementDetermine if series is absolutely, conditionally convergent or divergent {(-2n/(n+1))^(5n)}Determine if series is absolutely, conditionally convergent or divergent {(-2n/(n+1))^(5n)}Calculate the first eight terms of the sequence of partial sums {1/n^3}.  Converges or divergesCalculate the first eight terms of the sequence of partial sums {1/n^3}. Converges or divergesDetermine whether series converges or diverges e^n/(1 + e^(2n)). Use appropriate testDetermine whether series converges or diverges e^n/(1 + e^(2n)). Use appropriate testFind the second derivative of function y = cos^3 x.Find the second derivative of function y = cos^3 x.Label amplitude, phase shift, period for function y = 4 cos(x + pi/4).Label amplitude, phase shift, period for function y = 4 cos(x + pi/4).Find area of region bounded by polar curve r = cos theta in sector [0, pi/6]Find area of region bounded by polar curve r = cos theta in sector [0, pi/6]Evaluate definite integral ( sin sqrt(x))/(sqrt(x)) dx over [pi^2/9, pi^2/4] method of substitutionEvaluate definite integral ( sin sqrt(x))/(sqrt(x)) dx over [pi^2/9, pi^2/4] method of substitutionIdentify and graph polar equation r = 3 cos (4 theta). Rose with eight petals. Test for SymmetryIdentify and graph polar equation r = 3 cos (4 theta). Rose with eight petals. Test for SymmetryFind a formula for the nth derivative of function f(x) = 1/(x-1). SeriesFind a formula for the nth derivative of function f(x) = 1/(x-1). SeriesFind the indefinite integral for 3x^2 e^(2x) dx. Integration by PartsFind the indefinite integral for 3x^2 e^(2x) dx. Integration by PartsSketch region enclosed by curves x = 1-y^2 and x = y^2 -1. Find area of regionSketch region enclosed by curves x = 1-y^2 and x = y^2 -1. Find area of regionFind value of constants a and b of limit as x approaches 1 of (x^2 + ax +b)/(x-1) =5Find value of constants a and b of limit as x approaches 1 of (x^2 + ax +b)/(x-1) =5Use washer cross sections to find volume of solid revolving region about x axis, y = x+3, y = x^2 +1Use washer cross sections to find volume of solid revolving region about x axis, y = x+3, y = x^2 +1Determine if series converges or diverges (2+ sin(n))/(sqrt(n)^5). Direct Comparison TestDetermine if series converges or diverges (2+ sin(n))/(sqrt(n)^5). Direct Comparison TestFind Taylor polynomial of order 3 generated by f(x) = x^3-2x +4 at given point x =0 and x = 1 SeriesFind Taylor polynomial of order 3 generated by f(x) = x^3-2x +4 at given point x =0 and x = 1 Series
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