2. Show that the function u - p(sy) + Vj (y/2) provides the equation 0.

Q: Compute the values of dy and Ay for the function y= e4z + 5z given z = 0 and Az = dz = 0.02.

A: Given x = 0, dx = ∆x = 0.02            (1) Here y = f(x) = e4x+5x

Q: Find the linear approximation at x = 0 to Write your answer in the form y = Ax + BỊ.

A:

Q: 2. Show that the function u = p(xy) + Vry v(y/x) provides the equation = 0. dy? | dx²

A:

Q: 2. Show that the function u = e(xy) + VrY 4(y/x) provides the equation Pu = 0. dy? %3D -

A:

Q: -Find the D.f ofr (x, y) = (x² – y)' at Po(3, 1) with

A:

Q: 4. Find if y is a function of r defined implicitly by da 2*y + sin a = xe" + In

A:

Q: 1. Answer the following questions: (a) Find the linear approximation of y- f(x)-Vr at a 256 and (b)…

A: Firstly, we will calculate f'(x), then f(a), f'(a).

Q: 1 use the formula L = dt to find the length of the curve dt dt 1 X = y = t° for 0st s1

A: according to the guideline, we are allowed to answer the only the first question  please repost…

Q: Given f(x, y) = 3æ'y- 8ry. Compute: www dy?

A: This question can be solved using the concept of partial derivatives.

Q: 2. Show that the function u p(ry) + Vry v(y/x) provides the equation Pu = 0. ду? dx²

A:

Q: obtain the particular solutions satisfying the indicated conditions: dx/y=(25-x^2)^-1/2dy; y(0)=1

A:

Q: Write the general solution of the fourth-order DE y(4) – 2y" + y = 0 entirely in terms of hyperbolic…

A: We have to find the general solution of the differential equation y4-2y''+y=0. The auxiliary…

Q: dy 2- Find for the following function: dx А- у%3Dх*. сosx B- y= 2(secx)²

A: Given : A) y = x3·cosxB) y = 2secx2

Q: 2. Show that the function u = p(xy) + VTÝ v(y/x) provides the equation „Pu dx² 0. dy²

A:

Q: If the new DE is written in the form M(x, y) dx + N(x, y) dy = 0, one has My = || N, = X, Since M,…

A:

Q: Find the quadratic approximation at (0,0) for f(x,y) = e^(x+y) * (xy-1).

A:

Q: Find the derivative of the given function at P. (3, 3, 3) in the direction of u = 3i + 4j f (x, y,…

A:

Q: Find the linear approximation at x = 0 to Write your answer in the form y = Ax + B.

A:

Q: express in the form y = f (x) by eliminating the parameter x = t + 3, y = 4t

A: The given parameters are x=t+3, y=4t. The objective is to express in the form y=fx by eliminating…

Q: Find the ditterential of the function y = (x + 1(5x - 3). Sx-x-5 dy = (Sx - 3) *?+ 6x-5 (5x- 3)? dy…

A: Use the quotient rule of differentiation ddxuv=vdudx-udvdxv2. Power rule of differentiation…

Q: If y In(z- y) then y at the point where y = 0 is equal to

A:

Q: If y = f(x) is the solution of (5aty – 12a – 2y³)dx + (x³ + 4y³ – 6xy?)dy = 0, f(0) = 0, then

A:

Q: express in the form y = f (x) by eliminating the parameter  x = t 2, y = t 3 + 1

A: Given, parametric equation is:  x=t2,y=t3+1 Solution: x=t2,⇒t=±x     ...(1)y=t3+1 ⇒y=(±x)3+1…

Q: Find the value of ds/du at u = 2 if s = t^2 + 5t and t = (u2 + 2u)^(1/3).

A: Find ds/dt from s=t^2+5t

Q: 2. Show that the function u = p(xy) + Vry ý(y/x) provides the equation n, = 0. dy? U -

A:

Q: [-+] 5t dy 3.1는-51%3D-y dt

A: This is a linear 1st order differential equation.

Q: Compute the discriminant D(x, y) of the function. S(x, y) = x' + y* – 6x – 2y + 1

A:

Q: dw if: dt Q1) Using the chain Rule to find w = xy + 3z, x = sint, y 2 cost, z=t (x2 +)

A:

Q: Verify that the indicated function y = p(x) is an explicit solution of the given first-order…

A: This question can be solved using the concept of derivatives.

Q: Without eliminating the parameter, find d²y at t = 2 1 x = 1

A:

Q: wherey = x + C is a solution to this DE. What is the particular solution?

A: Let's find.

Q: Q1: Use Green's theorem to evalute f. (xy + y2)dx + x²dy by the curve y = x and y = x2.

A: Given problem:- Use Green's theorem to evaluate ∫c (xy + y2 )dx + x²dy  by the curve y = x and y =…

Q: The function f(z) = 1 has a poles at z = %3| ez – 1

A:

Q: Use the method of Example 4 to compute dy/dx p at P = (2, 1) on the curve y^2x^3 + y3^x^4 −…

A: we can solve by this implicit differentiation, so,

Q: 22. Find when t=, where x a(t + sint), y= a(I-cost) and a is a constant %3D

A:

Q: Find the quadratic approximation at (0,0) for f(x,y) = ln(1+x^2 + y^2).

A:

Q: If y = x(x – 1)* then y' at z = 2 is equal to

A:

Q: Find In(y') at the point (0, 1/e) where xy° – In(xª + y) = 1.

A:

Q: Determine the of : In (xy²) = x y dx

A: Derivative dydx of equation  lnxy2=xy

Q: 2. Show that the function u = p(xy) + Vxy v(y/x) provides the equation = 0. dy? -

A:

Q: Consider the function y defined implicitly by 3(x2 + y2)? = 100xy. Use the linear approximation at…

A: Given : 3(x² + y²) = 100xy

Q: Solve the following problem dw dw + x dt 1, -00 0, %3D dx with w(x, 0) = f(x).

A:

Q: ) Find the direction in which f (x, y) = x²+xyincreases most rapidly at P(1, –1).

A: 1.) given multivariable function is, fx,y=x2+xy and point is P(1,-1). Divergence: Divergence of the…

Q: Given f(x, y) = - (4x°y + xy® ). Compute: dy?

A:

Q: Express in form y=f(x) by eleminating the parameter x = e−2t , y = 6e4t

A: Here, x=e-2t and y=6e4t

Q: (b) If z = 9t²e 4t, find 4 dz dt

A: Given.

Types of Bias

Statistics is the study of data collection, organization, analysis, interpretation, and presentation. Statistical bias is a characteristic of a statistical technique or its findings in which the expected value deviates from the actual root quantitative parameter being estimated. According to the actual definition of bias, it refers to the tendency of a statistic to overestimate or underestimate a parameter.