4 - If w = x + 2y + z? , x =, y= r2 + In(s) , and z = 2r aw find at the point (r, s) = (-8,4). as %3D

Q: 20) Let y=7x+5x Then compute dy and Ay for X= -7 and dx =0.4. dy =? and Ay = ? Gounded 6o 4 decimal…

A: Derivative: - The derivative of the function is the equation that we find. The instantaneous rate of…

Q: Suppose f(0.25)=f(0.75)=b. If the Composite Trapezoidal rule with n=2 gives the value 4 for \int_0^1…

A: Introduction: The trapezoidal rule is a method to approximate a definite integral numerically. In…

Q: 7) if p(X) =- ) , and grea) =0; g'LW)=), Find f'la). %3D

A:

Q: (c) Show that (d/dz)z does not exist anywhere,

A: See the attachment

Q: Given: f(x, y, z) = y²³ In (x + 2) + ³x cash (yz) 9). Determine if the level curface of at k = 0…

A: The given function is: fx, y, z=y5lnx+z+3xcosh yz a) Determine the if the level curve at k=0 passes…

Q: The weight function for y"- y +3de* y = 0 is 3e* none O ex

A:

Q: Can i get help step by step please

A:

Q: 3 If y= Vx (x-1), find dy (Use rules, not a de finition XP

A: Given:         y=xx-1       dydx=ddxxx-1    Apply product rule:         ux·vx'=u'(x)·v(x)+u(x)·v'(x)…

Q: dy for y= In(In(2r')) dt

A:

Q: Show that y" + ay' = b, wherein a and b are constants, can be reduced to y' =+ C₁e-ax using…

A:

Q: A cylinder of radius r and height h has volume V = nr 2h.(a) Use the Linear Approximation to show…

A: Given: A cylinder of radius r and height h has volume V=πr2h a)  show:  ΔVV≈2Δrr+Δhhb)  Percentage…

Q: --- Q#3 Evaluate Cf 2x dV →Where E = {(x, y, z)| 0sys 2,0sx sV 4 - ,0 < z y} ,0 sz< y} Ee

A:

Q: ppose X1,...,Xn are i.i.d.U(0,θ). You want to test H0: θ=θ0 versus H1:θ < θ0 at level α? Derive the…

A: The given information is: Xi~U0, θ or fx=1θ,   0&lt;x&lt;θ The null and alternative hypotheses are:…

Q: Evaluate the bound of the error if the Trapezoidal rule applied to S (x)dx . Given that 5 k is…

A: Apply formula of trapezoidal error

Q: 6. Ifw = f(x-y, y-x), then show that, ar + L = 0. dx ay

A:

Q: 3) Find dz dy for z = e

A: Solution: As per given date   z=exy  For finding dz/dy , we assume that 'x' is a constant.

Q: (2) Evaluate 6y dV, where E = {(1, y, 1) | 0 < z < ry, 0 < y S 1, 0SISY} %3D

A: The objective of the question is evaluate the integral.

Q: Find dydx? for f(x, y) = eXy

A:

Q: p = m(1-dt) for d (buisness)

A: In this question , we can solve for 'd'.

Q: 4. Suppose that z = x³y, x= t², and y = t³, find . dt = 12t11 dt 11t10 b) = 10t° dt d) = 9t® dt

A: This question is related to differentiation, We will solve it using given information.

Q: What is the integrating factor of the linear DE of order one ydx + (3x - 2y +5) dy=0,

A:

Q: -Skatch the reglén of Etyndtion , reversed the order of itegral and evaluade dx dy 7 | +

A: We have to sketch and after changing the order of integration evaluate it.

Q: Find the Complete or Particular solution OF the Followoilng diffi rential equations: (2メコ+ )dx -2メよ…

A:

Q: 1. By using the following data compute the Karl Pearson's coeficient of corelation. EX=250, EXT =30,…

A:

Q: 4. Evaluate: S. yx²dx + xzydy + xz²dz, where C:x = sint, y = cost, z = t?, (0 <t< 1).

A: A line integral is the integral of a function along a curve. The function can be scalar-valued or…

Q: If f(x,v) = ex In(5xy) find dy?

A: Given: fx,y=ex2ln5xy. To find: ∂2f∂y2 Solution: In partial derivative we differentiate with respect…

Q: Find Homogeneous DE y'-ay=0

A: Given that: y'-ay=0

Q: 2. If f(x,y)= te Vy of=D0 then show) that 49 c) of af =0 dxay

A: Consider the given function. fx,y=1yex-y24y (i) First, we have to show that ∂2f∂x2-∂f∂y=0. First,…

Q: Find dy/dr by differentiating implicitly if z +ry- 6r = 2.

A:

Q: Use RK2 (Heun's method) with ħ = 0.5 to estimate y(1) given o: 8 Vū, y(t = 0) = 8, y' (t = 0) = 2.…

A: The Heun's method formula is The given values are h=0.5, y(0)=8, y'(0)=2 That is x0=0,y0=8 and…

Q: If y =Aex +Be™ d'y -(m+n) dy. Show that + mny = 0 dx

A:

Q: Eval S fCx,y,z)dV Por f auel regien W M, fory2)= 2x W: x'+ y? < zs 4

A: The region W : x2+y2≤z≤4, and f(x,y,z)=2x, we have to evaluate the value of ∬∫Wf(x,y,z)dV.

Q: Determine the value of the Wronskian W (y1, Y2) of y" – 2y +1 = e2 (x +1) if x=1.3 by using…

A:

Q: X+ xy B. Evaluafe the tripe in tagral S5* xy dydzdx,

A: As we know that: The Power Rule: ∫xndx=xn+1n+1+C ; n≠-1 (B). From the given integration:…

Q: 1. Find the saution YLEA oR Ele tntifial Value poobem y"-8y'+16y=8e*, yr0)=3,4'101=2,

A:

Q: Evample: y-xy, Yu)=1 and h:o.l a pproximale Y(1 3) using improved Euler Muthocd.

A:

Q: 8. If JM = x + 17 and MK = 5x – 23, find JL. %3D H. 'K

A: Note: There are multiple questions. No specific question has been asked.So, We will solve the first…

Q: 3ey , find Given z = dz dz au

A:

Q: Find nalytical salution to Pnti = (r+)+m possible. an Simplity as much as

A: Given equation is: Pn+1=r+1Pn+m⇒Pn+1=rPn+Pn+m⇒Pn+1-rPn-Pn=m

Q: Find the par ticular solution of the differencial 4. given x=0 and y= eguation dy -20cH1) (x+1)

A:

Q: Fand the anti daniahir of fw. e+e- 2Cosed px -

A:

Q: 9) A function y(x) is increasing and has upward concavity on the interval [-2, 3]. Would a…

A:

Q: 2. Compute ¡ E x dV , where E “ tpx, y, zq | x ď 0, z ď 0, x2 ` y 2 ` z 2 ď 9u

A: The given integral,

Q: 27. Find the length of the curve Vcos 2t dt y = from x = 0 to x = "/4.

A: The given curve is We know that by Second Fundamental theorem of calculus ,if F(x) is continuous on…

Q: Given z=3 In(t) and y=9t² then find dy de dy da %3D

A: We use parametric differentiation

Q: 4x 28. If R = and errors in x, y, z be 0-001. Show that the maximum relative error at x = y = z = 1…

A:

Q: Find dr dy at x = -1 if y =u° +5u – 4 and u = x² +x.

A:

Q: (b)/ Use the Trapezoidal Rule with n = 4 to estimate ſ,(x3 + 1)dx.

A: To find: ∫-11x3 + 1dx using trapezoidal rule with n=4

Q: Find, if y (3 z)t* + cosec (t) + Z In(2t + 3) dt2

A: First of all, let's get rid of Z by substituting Z = 43 in the equation above: y = (3 x 43)t4 +…

Q: Q3/ Evaluate Sz Vsinx dx, using i- Trapezoidal rule ii- Simpson's 3/8 rule Ans. 1.1615

A: 3 Given integral is ∫0π2sinxdx. i We have to evaluate the given integral by using trapezoidal rule.…

Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.