Given that 10x6 + 3x- x? f(x) : %D x2 a) Simplify f (x) b) Hence, or otherwise, find g(x) = | f(x) dx freods %3D c) The curve C with equation y = g(x) passes through the co-ordinate (0,1). Find the equation of C.

Q: 14. What is the slope of the curve at the point (0, x²+y-12r +4y = 5 %3D 0-2

A:

Q: An insect is in a toxic environment. The level of toxicity is given by T(x,y)= 2x* – 4y° If the…

A: Tx=0⇒x=0Ty=0⇒y=0Using D-TestD=TxxTyy-[Txy2]D=0 at (0,0)   T(x,y) is minimum

Q: d²y Solve the particular solution for = 2 – 4x when points (0, 2) and (-1, 3) are on the dx2 curve.

A:

Q: and the net is decribed by the equation y = V1 – x2 – z2, y 2 0,

A:

Q: Determine if the equation (dfferential form) is exact and find the solution if it is…

A:

Q: Suppose a cheetah is dashing due north at a rate of 30 m/s toward a popular watering hole, and a…

A: We need to find x(t),y(t),r(t) in the above question.

Q: In the given question , find d2y /dx2 implicitly in terms of x and y :-   xy - 1 = 2x + y2

A: In the given question , find d2y /dx2 implicitly in terms of x and y :- xy - 1 = 2x + y2

Q: Find the x- coordinate of the inflection point(s) of the | .2* curve y = -7xr'+ 4x +10.

A:

Q: Show that the function f(t) = 1² – } is a solution of the dif- ferential equation (y')² – 4y = 2.

A: Given:       f(t)=t2−12.Differential equation is: (y')2−4y=2

Q: Suppose that / (3x+-x²) dx=Ax³+ Bx³ +C, for constants A, B, C. What is the value of C if the curve…

A:

Q: The y, of y'"-y=2x2-x -3 by using variation of parameters is: .A Y,(x)= x - 1 .B y,(x)=x² + x +1 .C…

A:

Q: For y''+3y'+2y=e^-x, use the variation of parameters formula to find a particular solution. Show…

A:

Q: a) Find the general solution of the equation dªy dy dx² 4- x2 + 3e* - dr4 by using the method of…

A: As you have posted multiple parts,but they are independent so according to our guidelines we will…

Q: Solve using variation of parameters or reduction of order (D² – 3D + 2)y = (1+e²x)¯2

A:

Q: (a) For the solution that satisfies y(0) = 0, sketch the solution curve and estimate the following:…

A: (a) The solution curve with the direction field that satisfies the initial solution y0=0 is as…

Q: Find dy for the given values of x and Ax, y%3D5X²-6x, x= -2 and Ax =0.1 dy =D (Round to the nearest…

A:

Q: Find the particular solution of -4y = 3x – 1 given that when x=0, y=0 and d2x dx dx II

A:

Q: B. In each exercise, obtain the particular of solution. 2. y(9x - 2y) dx - x(6x – y) dy = 0; when x…

A: Differential equations

Q: Find the point thot maximites the f (xxy)= x*+ y 2. -6x+ 9 funcfion depending on the gCxy) zy -x²…

A: Consider the provided question,

Q: Use the method of Variation of Parameters to solve. SHOW WORK. y" – y' – 2y = 2e-t

A:

Q: 3. Find the length of the curve r = e® for 0ses 2n.

A: Given polar curv er=eθ   ; 0≤θ≤2π

Q: Using the variation of parameters, find the particular solution of (D2 +1)y = secx

A:

Q: Obtain the general solution unless otherwise instructed d²y 1. dx2 - y = 10sin²x

A: You have asked multiple questions and not mentioned which question answer you need so according to…

Q: 1. What is point-slope form? А) Ах + Вy %3D С y2 - Yı В) т%3 X2 - X, С) у - У1 %3 т(х - х) D) у %3D…

A:

Q: Use variation of parameters to find the particular solution to y'' + 5y' + 4y = 2e-34 Y(t) = […

A:

Q: Use the method of variation of parameters to solve y" – 4y +4y = 2e". %3D -

A:

Q: 2. Determine C when x-y%3D0 show the solutions. (xy + x)dx = (x²y2 + x² + y2 + 1)dy

A:

Q: Find general solution to Cauchy-Euler equation: (t^2)y''-2ty'-3y=t^2

A:

Q: V Solve usinog variaton of parameters or reduction of order (D²- 2D+1) y = e2"(e*+1)?

A: Solve by using variation of parameter  find auxiliary equation and then find wronskian and put in…

Q: Use an appropriate substitution to solve the equation z15 and find the solution that satisfies y(1)…

A:

Q: Solve the equation ru, + (x + y)uy = 1 %3D on dof:

A: In this question, we solve the partial differential equation by using characteristic method.

Q: | (3x+-x²) dx=Ax° + Bx² +C, for Suppose that %3D constants A, B, C. What is the value of C if the…

A:

Q: By making the change of variables u = 2, v = x, find the general solution of yfyy +fyx + fy = 1.

A:

Q: The equation f(x)= x² -e* has a solution [-1, 1]. With po= -1 p1=1, calculate p2 using the the…

A: The secant method uses the formula: xn+2=xn-f(xn)⋅xn+1-xnf(xn+1)-f(xn) to perform the iteration. The…

Q: The arclength of y 4x/2 for 2 < r < 4 is:

A:

Q: An insect is moving on the surface of a hot plate, the temperature of which at the point x units to…

A: Definition used-   To keep the temperature constant, the insect has to move in a direction that is…

Q: Find the value of d2y/dx2 at the point defined by the given value of t. x = t, y = square root 2t ,…

A:

Q: If the depth is given by the equation z = 3x2y + xy , the equation of the cutoff curve when x=1 is?…

A: If the depth is given by the equation z = 3x2y + xy , the equation of the cutoff curve when x=1 is?…

Q: Find the best quadratic approximation, Q(r, y) of V9 – 6x – 4y for (r, y) (0,0). near

A:

Q: (D³ + 2D² − 5D − 8)y = 0, when x = 0, y = 0, y' = 0, y = 2 - -

A: Given  (D3+2D2-5D-8)y=0 and when x=0, y=0, y'=0, y''=2. The formula for differentiation is…

Q: Suppose that/ (3r-x²) dr=Ax'+Bx'+C, for constants A, B, C. What is the value of C if the curve =…

A: Since you have asked multiple question As per our policy, we will solve the first question for you.…

Q: Find the equation of a line parallel to x = -8+ 2y that passes through the point (8, –2). Oy = -x –…

A:

Q: Find the isogonal trajectories to a family of straight lines y= cx that cut the lines of the given…

A:

Q: Solve the follawing systen. 2 x, - 5x - cost dt dx2 b) by using the method of unde termined…

A: Given system is dx1dt=2x1-5x2-costdx2dt=x1-2x2+sint First, let us solve corresponding homogenous…

Q: The equation of the tangent to the curve y = x4 – 4x3 + 2x? – 4x + 15 that is perpendicular to the…

A: topic - equation of tangent line to curve

Q: Find the equation of tangent line to the parabola y² = 6x – 3 which is perpendicular to the line x +…

A:

Q: The curve x = t - 3t, y = Vt intersects the y-axis when x = 0, which occurs when t = 0 and t = y 3-…

A:

Q: Use variation of parameters to find the general solution of y" – 2y' + 5y = e'.

A:

Q: A parabola has an equation of x² = 6y + 10. Compute the equation of a tangent to the curve which has…

A: Given that a parabola has an equation x2=6y+10. Here we have to compute the equation of a tangent to…