2. a) The area between the curve y= Vx,0 5x Sa and the x axis rotates around the x axis. Determine the constant a so that the volume of the rotary body is 10 volume units. Y = -4 4 -X-2 1 b) Calculate the area of the shaded area in the figure (intersection points can be read from the graph). X-2
Curve Sketching: Use the following guidelines to sketch the graph of y-f(x) x-5x (20 points) a. What are the behaviors of y when x->oo, or x--0? (3 points) b. What is the first derivative of this function? What are increasing intervals and decreasing intervals and max points and mini points? (6 points) c. What are the second derivative of this function? What are intervals for concavity upwards and concavity downwards and inflection points? (6 points) Use the above information (a,...
3. Using Curve Sketching methods, sketch the graph of the (x function y for -2T < x < 27T. Make sure that COS you include all steps, charts, and derivations details. 3. Using Curve Sketching methods, sketch the graph of the (x function y for -2T
10. Neatly sketch the region enclosed by the graph of y = Vx, the x-axis, and x = 3. Find the volume of the solid generated by revolving this region around the axes given below. (Use the method of your choice.) Set up an INTEGRAL and then evaluate it using your calculator. a.) About the x-axis b.) About the y-axis c.) About the line x = 4
Given, f(x) = {x #1, 2 5x<4 4,0<x< 2 (a) Sketch the graph of f(x) and its even half-range expansion. Then sketch THREE (3) full periods of the periodic function in the interval -12 < x < 12. (6 marks) (b) Determine the Fourier cosine coefficients of Ql(a). (10 marks)
3) Sketch the graph of the following rational functions. 2 a. f(x) = + +5r+6 x + 1 b. f(x) - 4x - 32 4) Solve each inequality. Give each solution in interval notation. a. + +8r+15 so b. 2x-5x > 3 C. (x - 1)(x+3)(x+5) > 0 x+3 d. > 0 x² - 5x+6 X +3 <2 2x+4 e.
2. Sketch a graph y = f(x) that satisfies the following criteria:3. Find the equations of any horizontal or vertical asymptotes of the following functions. 1. (x) = 26-5x + 7
find the area between the curve y=x^2+1 and y=x(2-x). sketch a diagram of this area. for what value(s) of n does y=x^n satisfy the differential equation: x^2(d^2y/dx^2)+5x(dy/dx)-21y=0
The region enclosed by y = Vx and y = 5x is rotated around the x-axis. Choose the integral that can be used to find the volume of the solid of revolution. & S (x - 12 ) dx = [" (432 – y") dy
s. Use the given graph of y f(x to sketch a possible graph of y - f'(x) and y-f"(x) (0,0) -1 6. Use the graph of y f'(x) to sketch a possible graph of y f(x) -2 31 I -2 s. Use the given graph of y f(x to sketch a possible graph of y - f'(x) and y-f"(x) (0,0) -1 6. Use the graph of y f'(x) to sketch a possible graph of y f(x) -2 31 I -2