MAT136H1 Chapter Notes - Chapter 2c-3a: Product Rule, Differentiation Rules, Good Luck!!

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25 Jul 2018

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MAT136H1 Full Course Notes

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= 0, = sin(), = 0: (sin2()) , (sin2()), . Consider the region lying between the curves = 4 and =2. For each line below, write an expression that approximates the volume of a slice with thickness" . Consider the region bounded by 2 and ( 1)2. Find the volume of the solid generated by rotating this region around the line = 1. Volume of a slice = 2(1 +)(2 ( 1)2) . Note : we chose to slice into pieces of width instead of to avoid rearranging equations. The shape of each slice can then be approximated as a cylindrical shell of thickness . total volume : 2. It is 2( + 1)(2 ( 1)2) Limits of integration where the 2 curves intersect which will be the range of allowed. = 0. 5 or = 2 using quadratic formula ( + 1)(2 ( 1)2) .

Related Questions

Want to ask: #11

Correct Answer: 11pi/30

p.s. one of the picture below is my calculating process, i have no idea where is the error

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

Solve all please.