MATH 1007 Lecture Notes - Lecture 18: Cube Root, Radian

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carmineraccoon722

6 Apr 2016

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Area with x as a funcion of y. A = int from c to d of [xright xlef]dy. To help us sketch this, use some key points. Recommended that we use: y = -3, -2, -1, 0, 1, 2, 3. Then sketch the two curves on the same plot. So the area in between the two funcions will be A = int -2 to 2 of [(4 y^2) (y^2 4)]dy. = int -2 to 2 of (8 2y^2)dy. = 8y (2y^3)/3 line from -2 to 2. We can do this same problem in a diferent way, like in last lecture. We can convert the whole funcion back to terms of x only if it is easy to do! Let s be a solid that has between x=a & x=0. Let a(x) be the area of the cross-secion in the plane p x through x & perpendicular to the x-axis, where a is a coninuous.

Related Questions

Let Q be the tetrahedron with vertices (0,0,0), (1,1,0), (0,1,0), and (0,1,1) and consider the triple integral { \int \int Q \int F(x,y,z) dV }
Rewrite the integral as an iterated integral in the indicated order. (*do not integrate*)
1. The order dz dx dy
2. The order dy dx dz
(Note: first come up with the equations for each of the planes that bound the tetrahedron. The bottom and side planes should be simple; the top plane is obtained by finding the equation of a plane given three points on the plane. Ensure the equation for the top plane is satisfied by the three points you know are in the plane before continuing.)
3. Suppose F(x,y,z)=1. Evaluate integral in #2.

whitesheep34

1. (45 marks) Short-Answer Questions. Put your answer in the box provided but show your work also. Each question is worth 3 marks, but not all questions are of equal difficulty. Full marks will be given for correct answers placed in the box, but at most 1 mark will be given for incorrect answer. Unless otherwise stated, it is not necessary to simplify your answers in this question. a) Find the equation of the tangent plane to the graph of the function z = f(x,y) = sell at (0,1). Answer b) Evaluate (T, 0) if f(x,y) = sin(ry). Answer c) Graph of a function z = f(x,y) is given by: Which of the following level curves correspondes to this function. Answer d) If f(x,y) = e(3x – 2y), find lim - Math)-f(x,y) e) Find % if f(x, y) = x2 - y3 and 2 = r sin(t), y = r cos(t). Answer f) Evaluate the directional derivative of f(x, y) = !at (1, -1) in the direction of u =(2, 1). Answer 8) Does Simono converge? h) Sketch the direction field of the differential equation = 1-2y. i) Consider the differential equation ay = 15 - 31, y(0) = 0, and use Euler's method with step size 0.1 to estimate y(0.1). Answer j) Knowing that (-3,-3) is a critical point of f(x,y) = 2:3 + y2 – 4.cy -3.0, use the second derivative test to find out whether it is a local minimum, local maximum, or a saddle point. Answer k) Solve the initial value problem, dy dt 642 2y + cos(u) y(1) = . Answer 1) Is ū=(2,2, -1) perpendicular to v = (5,-4, 2)? Answer m) Find the area between the graph of y = 1 + sin(x) and y=1-sin(x) from 0 to 7. Answer n) Determine the lentgh of the curve y = 8/2,0 SIS 3. Evaluate and simplify your answer. Answer o) Express the volume of the solid obtained by rotating the bounded region that lies between curves y = (x-2)2 and y=1,150 $4 about the vertical line 2 = 5. Do not evaluate this integral. Answer

MATH 1007 Lecture Notes - Lecture 18: Cube Root, Radian

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