Question 3: [25 pts] Answer the following questions. a) What is the first derivative of y...
Question 4: [25 pts] Consider the differential equation y" - 4xy = 0. a) Write the general form of the power series solution around Xo = 0 and find it's first and second order derivatives. b) Approximate the given differential equation using Power Series method by finding the first five terms of the Power Series solution around Xo = 0. c) How would your solution change if we change the differential equation as y" – 8y = 0? Explain.
For questions 3-8: 5y2 Let f(x, y) = + y 2 Find the two first partial derivatives and the four second partial derivatives of f at the point (1, -2). Question 6 Find fry (1,-2). Question 7 Find fy (1, -2). D Question 8 Find fy: (1, -2).
xy', + y,-xy = 0, x,-0 Answer the following questions a) What are the points of singularity for each specific problem? b) Does this ODE hold a general power series solution at the specific x0? Justify your answer, i) if your answer is yes, the proceed as follows: Compute the radius of analyticity and report the corresponding interval, and ldentify the recursion formula for the power series coefficient around x0, and write the corresponding solution with at least four non-zero...
3. Answer the following questions. Justify your answers. A. (&pts) Find the first three nonzero terms of the Taylor series of the function f(x) = px? centered at a = -1. B. (&pts) What is the Maclaurin series for f(x) = sin x? Use it to obtain the Maclaurin series for the function g(x) = x. sin 2x. C. (4pts) Suppose that f(2)= 1, f'(2) = 3, and f" (2) = -2. How can you use this information to estimate...
help 3. Answer the following questions. Justify your answers. A. (&pts) Find the first three nonzero terms of the Taylor series of the function f(x) = px? centered at a = -1. B. (&pts) What is the Maclaurin series for f(x) = sin x? Use it to obtain the Maclaurin series for the function g(x) = x. sin 2x. C. (4pts) Suppose that f(2)= 1, f'(2) = 3, and f" (2) = -2. How can you use this information to...
Help 3. Answer the following questions. Justify your answers. A. (&pts) Find the first three nonzero terms of the Taylor series of the function f(x) = px? centered at a = -1. B. (&pts) What is the Maclaurin series for f(x) = sin x? Use it to obtain the Maclaurin series for the function g(x) = x. sin 2x. C. (4pts) Suppose that f(2)= 1, f'(2) = 3, and f" (2) = -2. How can you use this information to...
4 problems using 1st and 2nd derivatives please solve question 6 to 10.Thanks Derivative Calculations In Exercises 1-12, find the first and second derivatives. 1. y = --x2 + 3 . 2. y = x2 + x + 8 3. s=58 – 375 4. w = 3z? – 7z3 + 2132 5. y = 4x3 = x + 2x - 6. y = x + x 2 + x cula 7. w = 322 – 17 8. s=-20 + 4...
Question 5 Answer the following questions What is the value of y when x is 15? y-10 + 2x If y is 10 what value is x? y = 10 + 2x What is the value of y when x is 10 and z is 2? y = 10+2x-2c what is the value of y when x is 0? y = 10 + 2x-2z What is the value of y when x is -5? y 10-6x +5z r
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,...
TICKET-IN-THE-DOOR Conceptual: Given a function z = f(x,y), write what the following notations mean in words. • 1x = 2t (partial denotion off wit x • ly =of sportial derivative off wit y) dy • 1. - 2f (2nd partial derivativt off wit > • ly = df (2nd portial derivative off wrt yo Practice: 1. Find the first-order partial derivatives of the following functions a. w -2xy + 5yVx+ 7y5 b. f(x,y) = ek + y Inx 2. Find...