Sketch the graph of the resulting function. 2. Solve a" +x = 8(t - ) -...
1. Sketch a graph of the following function: f(t)-5(H(t) -2H(t-1)+ H(t-2)) 2. Use the definiton of the Laplace Transform to show that -5s 3. Find the inverse Laplace transform of the following: (a) T(s)-( (b) Y(s)=式 ) (劫 +3s 4. Solve the the following initial value problem: Sketch the function, f(), and the solution vit) on the same graph. 5. Solve the the following initial value problem: y" + 144y = δ(t); y(0) = 0, ช่ (0) =0
you can skip question 1 Sketch the graph of x(t) sin(2t), y(t) = (t + sin(2t)) and find the coordinates of the points on the graph where the tangent is horizontal or vertical (please specify), then compute the second derivative and discuss the concavity of the graph. 1. Show that the surface area generated by rotating, about the polar axis, the graph of the curve 2. f(0),0 s asesbsnis S = 2nf(0)sin(0) J(50)) + (r°(®)*)de Find an equation, in both...
4. Find the general solution to the system x' = Ar, where A is as specified below. Make sure to write the solution in purely real form. 1 1 0 (a) A= ( -4 3 ) (1 -5 ) (b) A=1 (1 -3) 1 1 0 0 (c) A= | -2 1 2 1 -2 -2 1 ( -5 -3 (d) A= ( 7 ) 31 (You can skip part (d) as it is from $3.7.)
A9.5.36 Question Help Find a general solution to the system below. -2 x(t) x'(t) = This system has a repeated eigenvalue and one linearly independent eigenvector. To find a general solution, first obtain a nontrivial solution x, (t). Then, to obtain a second linearly independent solution, try x2 (t) = te"u, + e"u2, where r is the eigenvalue of the matrix and u, is a corresponding eigenvector. Use the equation (A - rl)u, = u, to find the vector u,....
3e-s 5e-257 Sketch the graph of the function : f(t) = 1+1 { + 6213 IS 52 s2 Solve the IVP, and write the solution as a piecewise function: y' +y = f(t), y(0) = 0, where f(t) = {1 0 <t<1 t > 1 -1,
math final 172 Problems 16-17 are worth 8 credits each 1 Let fx)9 and let ga)-1. Specity the domain of f(x)/slz). 2. Draw the graph of y 3cos 2x from z0to x-2 3. Draw the graph of y 4-+2. 4Write an equation of the line perpendicular to the line y-2r-3 through (4,1) and sketch its graph. 5. Draw the graph of y- -2r-2 and label its maximum 6. Draw the graph of y-V-I 7. In triangle ABC, side a-8 in.,...
Consider the following system. = x + y - 2 ot dy at = 5y = -2 at Find the eigenvalues of the coefficient matrix A(t). (Enter your answers as a comma-separated list.) 2= Find an eigenvector for the corresponding eigenvalues. (Enter your answers from smallest eigenvalue to largest eigenvalue.) K = K = K = Find the general solution of the given system. (x(t), y(t), z(t)) =
4. Find the general solution to the system ' = Ar, where A is as specified below. Make sure to write the solution in purely real form. (a) A = ( -_- :) (1) A= (1 -3). 1 0 (c) 0 (c) A= -2 -2 ( -5 1 2 -2 1 -3) (d) A= 3 1 (You can skip part (d) as it is from $3.7.)
8. Trace the graph of the function and sketch a graph of its derivative directly beneath b) a) c) Use any differentiation formulas to find equations of the tangent line and normal line to the curve y at the given point P a) y (2x -3)2 at P (1,1) b) y (2+x at P (0,2) 9. 10. The graph of f is shown. a) State, with reasons, the numbers at which f is not continuous. b) State, with reasons, the...
please explain and do in matlab Problem 3. Consider the function f(x) e cos(2r). (1) Sketch its graph over the interval [0, m) by the following commands: (2) Using h = 0.01 π/6 in [0, π]. The commands are: to compute the difference quotient for z And the difference quotient is: ( 6 (3) Using h-0.01 to approximate the second derivative by computing the difdifquo for in [0, π). The commands are: And the difdifquo is: Problem 3. Consider the...