Q2) By using the Lagrange interpolation method, estimate the value of y(0.5) where y(3) = 0.62 , y(6)=0.55?

Q: 7x – 4xy = C

A:

Q: Q4 If f (x, y) = x sin y + ey asf ax2ay3 Find

A: Let's find.

Q: Z is the midpoint of VY and X is the midpoint of WY. If VW = s + 47 and XZ = s, what is the value of…

A: Given,          Z is the midpoint of VY¯ and X is the midpoint of WY¯ .           VW=s+47 and XZ=x…

Q: 8) Find the value of x that makes line m || line n. 120 3x E AS

A: “Since you have posted a question with multiple sub-parts, we will solve the first three subparts…

Q: What is t' (x) if t(x) = ? ez

A:

Q: The spread of a virus is modeled by V(t) = -t° +t² + 12t, where V(t) is the number of people (in…

A:

Q: 3. Find the average height of a point on the semicircle y =4- x over the interval -2 < x S 2.

A:

Q: Trapezoid JKLM is shown below. y 4 К (2, 3) L (4, 3) 1 (1 1) M(5 1) 3. 2.

A:

Q: Find the equation of the normal line (NL) to the graph f(x)=x³ – 4x atx = 3 .

A: We need to find derivative.

Q: Let X; = tB¡ B,ds. | Is (X,)r20 a F - martingale?

A: Consider the given process:        Xt=tBt-∫0tBsds

Q: Find the extreme values of f(x, y) = x² + 2y² subject to xy = 4 using Lagrange multiplier method.…

A: Here we have to use the Lagrange multiper method

Q: Which is the linear differantial equation into which the Bernolli differantial equation transforms

A:

Q: Use the trapezoidal rule to find AT using the indicated value of n. 8 dx; n = 8 2x2 +2

A:

Q: Q2: Prove that: d csc-(InVx) dx -

A: The main objective is to prove ddxcsc-1lnx=-12xlnxlnx2-1. It is known that ddxcsc-1x=-1xx2-1.

Q: The linear approximation at x and where B is:

A: Given a trigonometric functionf(x)=sin(6x)

Q: 7. For what values of m does the function y = e™* satisfying the following equation y" – 3y' – 10y =…

A: We have to find the values of m.

Q: Use the Midpoint Rule with m = n = 2 to estimate the value for 4x + 2ydA on the rectangle R = [0, 8]…

A:

Q: z) = 8x? In (5y + 9z). Find the range of tl %3D

A: We have to choose the correct option according to the given option

Q: P is the midpoint of GH implies that GH = 2PG.

A: We have to prove that GH=2 PG if P is the midpoint of GH. Drawing the figure of given condition, we…

Q: 10, 6J. the Midpoint Rule with timate the folllowing. IL x. v) da How could you improve your…

A: As m=n=2 Therefore let us take the subintervals as: 0,3 and 3, 6 The midpoints od these subintervals…

Q: 2) What is the relationship between 2J andOZK? K Supplementary Adjacent Vertical Complementary…

A: If sum of two angles is 90 degree. Then the angles are called complementary.

Q: 3. Evaluate f 2xdx + (y + 2)dy along the rectangle with vertices (0, 0), (0,3), (3,3) and (0, 3).

A:

Q: Identify the transacation of point P x + 3, y + 1). ddf2d92a ddf892d342a ddf892d342a dd1892d342a…

A:

Q: Use Lagrange multipliers to maximize the function x, y) subject to the constrai x.)-Say, Sy 20

A:

Q: 3. Fimd the exact atea of the Sure Pace curve y=V5-x 3{x55 by Yotating the our X-aris.

A: The given curve is  y=5-x  ; 3≤x≤5

Q: Use the Midpoint Rule with m = n 2 to estimate the value for 5 x + 3ydA on the rectangle R = (0, 8]…

A: Given fx,y=5x+3y

Q: Find the zeYo k its ovdev for Sunction f2)=1-Ti + Z+ e.

A: Given the function, f(z)=1-πi+z+ez. Now, in order to find the zero of the function f(z), we will…

Q: Find the orthogonal trajectories of the family of x² – y? = cx = CX -

A:

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

A: Given that, y=cx.

Q: Find the particular sölution f"(x) = 4, f'(2) = 12, f(2) = 17

A: integration 2 times and after applying initial condition we get f(x)

Q: What is the relationship between ZW and ZX? 3,

A:

Q: B- Use the Trapezoidal rule with n=2 to estimate fdx, to find the absolute relative true error |E¿|?

A: In this question we have to use trapazoidal rule to find integral.

Q: Q2 by using Simpsons Rule method to find ,n=6 5 1 dx х 2

A: use sub interval for finding the integral.

Q: 5 B) Find y" for the function y = x + Vx at p(1,3)

A: Given query is to find the double derivative of the expression at point p.

Q: Use the Midpoint Rule with m = n = 2 to estimate the value for 4x + 3ydA on the rectangle R = [0, 8]…

A:

Q: Use Lagrange interpolation to approximate y at x=c from the following tabulated values: C+3 Y3 C-1…

A: We know the Lagrange interpolation polynomial is…

Q: Given f(*, y) = 8a'y - 4cy. Compute:

A:

Q: 5. Find the local extreme values of f(x, y) = x²y on the line a +y = 3.

A:

Q: Find the R.M.S. value of Jlogx over the range x = 1 to x = e.

A:

Q: f(x, -0.0494 -0.3662 etter estimates by using Ar = 0.01 and Ay = 0.01. %3D 0.0516

A: Here we have to use difference quotients with ∆x=0.1 and ∆y=0.1 to estimate the fx(1,3) and fy(1,3)…

Q: 2. Use the secant method to estimate the root of f(x) = a° + a³ + 3. %3D By starting with the…

A:

Q: Find the 2nd solution using reduction of order. xy" +y' = 0; y1 = Inx For the toolbar, press ALT+F10…

A: Just I have used the method of reduction of order and solve in detail and find that  Second solution…

Q: 4.1 Use the trapezoidal rule to find an approximate value for V1+x'dx with n = 4.

A:

Q: Find the G.S. about xo = 0 for: (x² + 4)y" + xy = x + 2

A:

Q: 10 Q5/ Evaluate x*dx ,n 5, using trapezoidal rule.

A: The trapezoidal rule formula is: ∫abf(x)dx≈∆x2f(x0+2f(x1)+2fx2+...+2fn-1(x)+f(xn))...(1) where,…

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: