(a) Evaluate: L (2+5x)e 'dx 9Marks (b) Determine the area enclosed between the curves y =...
(a) Evaluate: L (2+5x)e 'dx 9Marks (b) Determine the area enclosed between the curves y = x + 1 and y = 7-X 8Marks (C) Water is leaking from a pipe and the volume. V litres, of the water is decreasing at the rate (6-21) litres per minutes after t minutes. Assuming that V = 9 when t = 0, find V in terms of t. 7 Marks (d) Find the equation of the curve that passes through (26) If...
(a) Evaluate: L (2+5x)e 'dx 9Marks (b) Determine the area enclosed between the curves y = x + 1 and y = 7-X 8Marks (C) Water is leaking from a pipe and the volume. V litres, of the water is decreasing at the rate (6-21) litres per minutes after t minutes. Assuming that V = 9 when t = 0, find V in terms of t. 7 Marks (d) Find the equation of the curve that passes through (26) If...
[11 Marks) ii) Determine the shaded area enclosed between the given two curves 3 +2, y = x + 2 4 y =
Suppose C is a curve parametrized by r(t)=<cost,sint,1> and S is the portion of z=x^2+y^2 enclosed by C, located in the vector field F=<z,-x,y>. 25. Suppose C is the curve parametrized by F(t) = (cost, sint, 1) and S is the portion of z = x2 + y2 enclosed by C, located in the vector field F = (2, -,y). Verify Stokes' theorem. That is, find show they are, in fact, the same. fe dr and SIC (curl ) ñds...
whats the area? Sketch the regions enclosed by the given curves. y = VX y = 2x X=25 y y 8 8 6 6 4 15 20 5 10 25 10 15 20 25 у Lenovo c x DE F1 Esc F7 FO FB FS F6 F2 F * ) # 3 $ 4 & 7 2 01 6 9 8 w R T Y U 8 B 6 6 10 15 20 25 5 10 15 20 Find its...
Question 2: Find for the following functions: (1) y=-42x2-3x -! 7x? -5x + 9 (3) y= x+5 (5) Y= 7+3 (y = (3x* + 3x + 2)(x+1) (7) y =(5x + 7x) Page 1 of 2 Question 3: (0) Find the slope of the graph of y=f(x) = 3x - 6x +1 at the point (2,1) (ii) Find the equation of the tangent line to the curve y = f(x) = x*-10x2 + 9 at x=-1 (iii) Find the equation...
2. Evaluate the following indefinite integrals: (a) vel V=(x+2) dx ET (b) 3. Evaluate the following definite integrals: (a) cos(x) da (sin(x) +18 (b) COS 4. The graph of y=g(t) is shown below, and consists of semicircles and line segments. y=g() -1 3 6 596 s(t) dt Define the function f(x) by f(x)= Use the graph of y = g(t) and the properties of the definite integral to find: (a) the value of (i) f(3) (ii) f(-1) (iii) 1'(6) (b)...
2 and 4b please e Iheorem 13.2.1 to prove that it is a A firm produces two different kinds, A and B, of a commodity. The daily cost of producing Q its of A and Q2 units of B is C(Q1,02)-0.10 +0102 +Q. Suppose that the firm sells all its output at a price per unit of P1 120 for A and P290 for B. (a) Find the daily production levels that maximize profits. (b) If P2 remains unchanged at...
12 10. Find the area enclosed by the polar curve 2 11 cos (80). 11T Hide Elapsed: 0000 27 Instructions O22π 11. This question is worth 20 points. You must complete both parts. Parts (a) and (b) are not related and should be answered as separate, distinct problems. θ2,0 θ (a) (10 points) Graph the polar curve r (b) (10 points) Find the surface area given by rotating the curve ya froma1 to 3 about the z axis. 12. This...
All of 10 questions, please. 1. Find and classify all the critical points of the function. f(x,y) - x2(y - 2) - y2 » 2. Evaluate the integral. 3. Determine the volume of the solid that is inside the cylinder x2 + y2- 16 below z-2x2 + 2y2 and above the xy - plane. 4. Determine the surface area of the portion of 2x + 3y + 6z - 9 that is in the 1st octant. » 5. Evaluate JSxz...