4. Find the value of x(0.3) for the coupled first order differential equations together with initial conditions dx x(0) 0 and y(0)=1 sint, dt 4. Find the value of x(0.3) for the coupled first order differential equations together with initial conditions dx x(0) 0 and y(0)=1 sint, dt
determine whether each integral is convergent or divergent 1- 1/(x-2)^3/2 dx, limits ( infinite to 3) 2- (1/3-4x)dx, limits (0 to -infinite) 3- e^(-5p) dx, limits ( infinite to 2) 4- (x^2/(sqrt(1+x^3)))dx , limits ( infinite to 0) 5- lnx/x dx , limits(infinite to 1) 6- 1/(x^2 +x)dx , limits (infinite to 1) 7- 3/x^5 dx ,limits (1 to 0) 8- dx/(x+2)^1/4 , limits (14 to -2) 9- 1/(x-1)^1/3 , limits (9 to 0) 10- e^x /((e^x) -1), limits (1...
ENG 1005 ASSIGNMENTI QUESTIONS (1) Use integration by parts to calculate sin(In(x) dx and Here, In is the natural logarithm. cos(In(x))dx. [5 marks (2) (a) Use integration by parts on sinh(t) sinh(t)dt and the identity cosh (1) = 1+sinh'in to calculate the integral of sinh(r). (b) Calculate the integral of sinh(r) by expanding the product and then integrating, Confirm that you get the same answer as in part (a). (e) Show that if x is a positive real number, then...
(1 point) Consider the system of differential equations dx dt = -1.6x + 0.5y, dy dt = 2.5x – 3.6y. For this system, the smaller eigenvalue is -41/10 and the larger eigenvalue is -11/10 [Note-- you may want to view a phase plane plot (right click to open in a new window).] If y' Ay is a differential equation, how would the solution curves behave? All of the solutions curves would converge towards 0. (Stable node) All of the solution...
Question 2 (Learning Outcome 2) 0 S (*x+3) dx S A) Evaluate the following integrals. 4x+7 2x+5) 5x2–2x+3 (ii) dx (x2+1)(x-1) x2+x+2 (iii) S3x3 –x2+3x+1 dx dx (x+1)V-x-2x In (x) dx (iv) S x2 X+1 (vi) S dx (1+x2) (vii) S dx x(x+Inx) (viii) Stancos x) dx (ix) 30 Sin3 e*(1 + e*)1/2 dx dx 2 sin x cos x (x) S B) Find the length of an arc of the curve y =*+ *from x = 1 to x...
10. Trapezoidal Rule is used to approximate the integral f(a) dx using 1- (yo +2y1 + 2y2 + x-na b-a + 2yn-1 +%),where Use this approximation technique to estimate the area under the curve y = sinx over。 a. π with n 4 partitions. x A 0 B: @ Δy B-A b. The error formula for the trapezoidal rule is RSL (12ba)1 where cischosen on the interval [a, b] to maximize lf" (c)l. Use this to compute the error bound...
arcsin x dx Hint: Use integration by parts. 2. Find the arc length of the portion of the parabola y = 10x - x that is above the x-axis. Find the volume of the solid of revolution if the region between the curves 3. 4. y = x and y = 4x is rotated about the x-axis. Find the area under the curve defined by the experimental data below by using Simpson's rule. MAT2691/101/3/2019 5. Simplify 3 -2 7 4...
13. Integrate: a. j«x+278)dx 0 b. (dx х c. dx 9+ x d . xdx? +2 dx 2x+1 хр '(x’+x+3) f. I sin (2x) dx g. cos (3x) dx h. ſ(cos(2x)+ + secº (x))dx i. [V2x+1 dx j. S x(x² + 1) dx k. | xe m. [sec? (10x) dx 16 n. .si dx 1+x 0. 16x 1 + x dx 5 P. STA dx 9. [sec xV1 + tan x dx 14. Given f(x)=5e* - 4 and f(0) =...
dx/dt = 4x -x^2 -2xy dy/dt = -y+0.5 xy a) find equilibrium points b) find Jacobian matrix for above system c) find Jacobian matrix at eq. point (0,0) d) draw phase portrait near (0,0) from © e) show at eq. point (4,0) the Jacobian matrix is -4 -8 0 1 f) draw phase portrait near (4,0) from (d) g) at eq. point (2,1) the Jacobian matrix is -2 -4 0.5 0 h) draw phase portrait near (2,1) from (f) i)...
2. Evaluate the following indefinite integrals: (a) vel V=(x+2) dx ET (b) 3. Evaluate the following definite integrals: (a) cos(x) da (sin(x) +18 (b) COS 4. The graph of y=g(t) is shown below, and consists of semicircles and line segments. y=g() -1 3 6 596 s(t) dt Define the function f(x) by f(x)= Use the graph of y = g(t) and the properties of the definite integral to find: (a) the value of (i) f(3) (ii) f(-1) (iii) 1'(6) (b)...