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3253Tangent Plane to a Product SurfaceFind the tangent plane to z=xy at (2,3,6).数学中等derivation未尝试面试订阅3254Linearization of a Logarithmic SurfaceFind the linearization of f(x,y)=\ln(x+y) at (1,1).数学中等derivation未尝试面试订阅3255Tangent Plane to a Three-Variable SurfaceFind the tangent plane to w=x 2+y 2+z 2 at (1,1,2,6).数学中等derivation未尝试面试订阅3256Classify the Origin for x^2+2y^2Classify the critical point at the origin for f(x,y)=x 2+2y 2.数学中等derivation未尝试面试订阅3257Classify the Origin for x^2-y^2Classify the critical point at the origin for f(x,y)=x 2-y 2.数学中等derivation未尝试面试订阅3258Classify the Origin for -x^2-4y^2Classify the critical point at the origin for f(x,y)=-x 2-4y 2.数学中等derivation未尝试面试订阅3259Classify the Origin for x^2+xy+y^2Classify the critical point at the origin for f(x,y)=x 2+xy+y 2.数学中等derivation未尝试面试订阅3260Classify the Origin for -x^2+2xy-y^2Classify the critical point at the origin for f(x,y)=-x 2+2xy-y 2.数学困难derivation未尝试面试订阅3261Area of an Ellipse from the Unit DiskThe map x=2u,\ y=3v sends the unit disk u 2+v 2\le 1 to an ellipse in the (x,y)-plane. What is the area of that ellipse?数学中等derivation未尝试面试订阅3262Area of a Parallelogram from a Unit SquareThe map x=u+v,\ y=u-v sends the unit square 0\le u,v\le 1 to a parallelogram. What is its area?数学中等derivation未尝试面试订阅3263Integral After a Simple ScalingUse the change of variables x=2u,\ y=3v to compute \iint R 1\,dx\,dy, where R is the image of the rectangle 0\le u\le 1,\ 0\le v\le 2.数学中等derivation未尝试面试订阅3264Area Scaling Under a Triangular MapThe map x=u,\ y=u+2v sends the unit square to a parallelogram. Compute the image area.数学中等derivation未尝试面试订阅3265Area of a Polar WedgeUse the polar Jacobian to compute the area of the region 0\le r\le 2,\ 0\le \le /3.数学中等derivation未尝试面试订阅5850Alternating Geometric SumEvaluate the infinite series sum (n=0) inf 5 * (-2/3) n.数学简单数值题未尝试免费5851Telescoping Log Partial SumFind the value of the partial sum S N = sum (n=1) N ln(1 + 1/n), and state whether the full series converges.数学简单数值题未尝试免费5852Nested Radical Fixed PointA sequence is defined by x 1 = 1 and x (n+1) = sqrt(2 + x n). Assuming it converges, find its limit.数学中等数值题未尝试免费5853Radius of Convergence via Ratio TestDetermine the radius of convergence of the power series sum (n=1) inf (3 n / n) x n.数学中等数值题未尝试免费5854Reciprocal Product SeriesEvaluate the infinite series sum (n=1) inf 1 / (n(n+1)).数学简单数值题未尝试免费5855p-Series Convergence ThresholdFor which of the following exponents p does the series sum (n=1) inf 1/n p converge: p = 1/2, p = 1, p = 3/2, p = 2? List all values for which it converges.数学简单数值题未尝试免费5856Compound-Limit ExponentialEvaluate the limit of the sequence a n = (1 + 3/n) n as n -> inf. Give the exact value and a decimal to three places.数学中等数值题未尝试免费