someone please help me solve this question 5(a,b,c). thank you!!! 5.) Consider the function f(x) =...
only number 5-7. Just set up no solve. show all work 1) Rotate the area bound by f(x): 2x + 1, y : O, x-1, and x : 4 around the x- 2) Rotate the area bound by y : x2 , y :0, and x-2 around the y-axis. #3-7: Draw a graph and setup the integral, including boundaries for determin the solid created. You do NOT need to evaluate the integrals. 3) Rotate the area bound byy and ya...
I need help with this question, thank you! (1 point) Consider the function f(x, y) = e-4x-x?+8y=y2. Find and classify all critical points of the function. If there are more blanks than critical points, leave the remaining entries blank. fx = fy= fxx fxy fyy = The critical point with the smallest x-coordinate is ) Classification: ( (local minimum, local maximum, saddle point, cannot be determined) The critical point with the next smallest x-coordinate is ) Classification: ( (local minimum,...
2. (a) Obtain and classify all stationary points and point of inflection of the function f(x) = 4x3 – 22x2 + 40x – 25. [5 marks) (b) Sketch the function y = f(x) showing all x and y intercepts, stationary points and point of inflection. One of the factors of f(x) = 423 – 22cr2 + 40x – 25 is (r – ). [2 marks] (c) Evaluate the definite integral of f(c) on the domain 2 € (0,6]. [3 marks)
Instructions: Show all your work for FULL credit. Calculators are NOL final answer. Neatness is highly appreciated. 1. A region R, bounded by y 2x, y 6-x, and x-axis, is rotated around the y-axis. Sketch the region R, in the box a) 15 strip/slice you will use to find the volume of the solid of revolution. b) Write the definite integral that gives a X the volume of the solid of revolution. (DO NOT evaluate the integral.) Find the circumference...
(a) A function / has first derivative f'(z) = and second derivative 3) f"(x) It is also known that the function f has r-intercept at (-3,0), and a y-intercept at (0,0) (i) Find all critical points, and use them to identify the intervals over which you will examine the behaviour of the first derivative ii) Use the f'(), and the First Derivative Test to classify each critical point. (ii) Use the second derivative to examine the concavity around critical points...
can you please solve all the questions 4 a) Find fx) dx using the Left-hand Sum. ONote ar is not 2 1 consta) fx) 5.75 9.5 12 14 b) Sketch the rectangles used to evaluste the definite integral in a) 10 Evaluate the definite integral using the Right-hand Sum e) fn The regions A. B, and C in the figure above are bounded by the graph of the function fand the a-axis If the area of each 5. region is...
Please solve for part (b) and (c) thank you! 1. Consider the function f(x) = e-x defined on the interval 0 < x < 1. (a) Give an odd and an even extension of this function onto the interval -1 < x < 1. Your answer can be in the form of an expression, or as a clearly labelled graph. [2 marks] (b) Obtain the Fourier sine and cosine representation for the functions found above. Hint: use integration by parts....
Need some help for this question 5) Use Desmos to graph the region in the first quadrant that is bounded between the graphs of y=x+2, y = 3, and the y-axis. Then answer the following questions. a) (2 pts) Create a rough sketch of the region on your paper, and show an appropriate representative slice on your diagram that could be used to find the volume of the solid generated by rotating this region about the x-axis. b) (2 pts)...
I lost in this I need help please thank you 13) [6;10] Given F(x, y, z)=(-2yz, y, 3x), and C is the curve of intersection of z = 3x² +3y2 and z=3. Sketch a representative drawing. Assume C has counterclockwise orientation when viewed from above. (a) SET UP the line integral (F. dr as a line integral with a parameter t. Your final integral should be a с single integral in terms of t only, including the bounds of integration....