7. Applications of Differentiation 7.1 Position and Velocity 7.1.1 Acceleration and the Derivative 7.1.2 Solving Word Problems Involving Distance and Velocity 7.2 Linear Approximation 7.2.1 Higher-Order Derivatives and Linear Approximation 7.2.2 Using the Tangent Line Approximation Formula ...
a technique of integration that allows the exchange of one integral for another using the formula ∫udv=uv−∫vdu∫udv=uv−∫vduintegration by substitution a technique for integration that allows integration of functions that are the result of a chain-rule derivativeintegration...
Example: Finding the Center of Mass of a Lamina LetRbe the region bounded above by the graph of the functionf(x)=√xf(x)=xand below by thexx-axis over the interval[0,4].[0,4].Find the centroid (center of mass) of the region. Show Solution Try It LetRRbe the ...
答案: 73.Find the integration formula of the area of the region bounded above by the curve【图片】, below by the curve【图片】, on the left by【图片】, and on the right by【图片】. 答案: 74.If【图片】is continuous on [-1,1] and the average value is 2, then【图片】 答案: ...
We revisit the interplay between the mass, the center of mass and the large scale behavior of certain isoperimetric quotients in the setting of asymptotically flat 3-manifolds (both without and with a non-compact boundary). In the boundaryless case, we first check that the isoperimetric deficits...
Projection of Vector A on Vector B P & Q Vector Points| Position Vectors | Projection of a on b, b on a | Speed Quadratic Formula Sketch a Graph| r(t) function | Make a Table of Points Surface Integral| x,y | x,z | y,z ...
Therefore, from Formula 15.7.13, the mass of is EXAMPLE 2 Evaluate . SOLUTI ON This iterated integral is a triple integral over the solid region and the projection of onto the -plane is the disk . The lower surface of is the cone and its upper surface is the plane . (See Figure...
observing the minute and elusive with the powerful microscope of his Infinitesimal Analysis; observing the elusive and vast with the limitless telescope of his Calculus of the Infinite; making guesses regarding the order and internal harmony of the data observed and collocated; testing the hypotheses,...
Giveexamples. 3.Howaredoubleintegralsusedtocalculateareas,averagevalues, masses,moments,centersofmass,andradiiofgyration?Give examples. 4.Howcanyouchangeadoubleintegralinrectangularcoordinates intoadoubleintegralinpolarcoordinates?Whymightitbe worthwhiletodoso?Giveanexample. 5.Definethetripleintegralofafunction...
7. Applications of Differentiation 7.1 Position and Velocity 7.1.1 Acceleration and the Derivative 7.1.2 Solving Word Problems Involving Distance and Velocity 7.2 Linear Approximation 7.2.1 Higher-Order Derivatives and Linear Approximation 7.2.2 Using the Tangent Line Approximation Formula ...