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Multiple choice questions Question 1 The graph of y=5 + 9x - 2r2 (24, 154) (22...
2r2-3ry equation for the tangent plane to the graph of f(x, y) (2, 1). 5. Find an at (r, y)
2r2-3ry equation for the tangent plane to the graph of f(x, y) (2, 1). 5. Find an at (r, y)
te tt 9 Let S be the surface defined by r2 y-22= 1 and 0 15 points by the normal direction toward the z-axis. Find the flux of the velocity field V 1and oriented (z2-ry2)i+(2.2y -yz2)j+ (y2z- 2r2)k across S Solution. To use Gauss Theorem, define C and C2 such that C1 {(a, y, z ) | a + y? < 2, z = 1} C2={(r,y,)| +y1.0} 11 TALK X W P S ww F6 & # 2 3 4...
a. graph f(x)=2x^2-3x+4 by determining whether its graph opens up or down and by finding its vertex, axis of symmetry, y-intercept and x-intercept b. determine the domain and the range c. determine function is increasing or decreasing
g) Sketch the graph of f(x) h) Determine the minimum or maximum value of the function. i) State the domain and the range in interval notation. 1. Given f(x)-2-3x (7 points) a) State whether the graph of the parabola opens upward or downward. b) Identify the vertex using the vertex formula. c) Determine the x-intercepts d) Determine the y-intercept. e) Determine the axis of symmetry ) Write the equation of the function fit) in vertex forrm
g) Sketch the graph...
Q3 (5 Marks) Find the values of x and y such that {(x + yi) =(-1 + 71)2 04: (6 Marks) Let Z2 = 5 + 7j a) Find the modulus and the argument of Zz. b) Express 2, in polar form r cose + r sino ; Q5. Let f(x) = 6x2 - 2x - 3, part of the graph of funtion shown below. (1+1+2 Marks) (a) Draw the graph of y = 2 on the same axis. (b)...
3. Determine the equation of the function graphed to the right: [3 Points) YA 20 16H 12 8H 4 (1,5) (0.1) f(x) = -3 2-1 1 2 3y=0 4. Determine whether the following are symmetric about the x-axis, y-axis, and/or origin. Answer 'Yes' or 'No' to each prompt below. [6 Points) b) x = y2 +3 3+ 2- 1- 4-3 -2 -1.11 1 2 3 -2- -3 x-axis Symmetry? x-axis Symmetry? y-axis Symmetry? y-axis Symmetry? Symmetry about origin? Symmetry about...
3. Graph: f (x)=\x2-4 4. Use the calculator to determine: $(x) = 3x² - 12x +4 10 9 A) vertex: 7 5 B) y-int: 2 C) opens: . -10 -10-387-5 -1 0 1 2 3 4 5 6 7 8.9 10
By 5. (a) Verify that y = {24 sin x is a solution to the differential equation dx2 dy + 5y = 0. dc [10 marks) (b) Differentiate the following functions with respect to c: (i) In(1 + sin? 2) (ii) * 2x3 - 4 - 8 dc. (c) Evaluate the integral / 272 * +432 – 4.7" [15 marks] [25 marks] 6. (a) let f: R+R be a function defined by f(x) 3 + 4 if : 51 ax+b...
y (m) 4 nC 0 -10 nC 8 nC -5-3-1 01 2 3 4 5 What is the magnitude of the resulting -10 nC charge at the ori- force on the gin? The value of the Coulomb constant is 8.98755 x 109 N C2/m2 Answer in units ofN 012 (part 2 of 2) 10.0 points What angle does the resultant force on the 1 x 10-8 C charge at the origin make with the positive r axis? Quadrant I lies...
1. A, on a coordinate axis (1)sketch x? + (y – 5)2 = 9, (2)describe the graph, (3)the graph is revolved about the x-axis, set-up integral which will compute its VOLUME, simplify the integrand as much as possible but DO NOT DO THE INTEGRATION. B. The triangle whose vertices are (0,0), (2,8) and (2,2) is revolved around the (a)x-axis, (b)y-axis (1)find the eqs. Of the sides, (2)draw graph, (3)compute (a) and (b) C. A student on test was asked to...