Directions: Select the correct answer(s). Which is/are equivalent to 32 y'z167 Select all that apply. 8xy'z 8x y"z" 12.284 128y'z" 2xy'ye 32 x*y*z" 2ya d/2xy

Q: (개) -3 dy 3yz

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Q: Exact ODE y'sin2nx-nycos 2rx

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Q: (1) y = 12 – x², y = x² – 6 (2) y = sec? (x), y = 8 cos(x) --- The range for x is from -60° to 60°…

A: As per guidelines we arpposed to answer Only 3 subparts (if there are multiple sub parts asked) Only…

Q: differenti en y(2) =

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Q: Qg show that: coths =} hm X+1/, X-1

A: Formula: The relation between hyperbolic function cothx and exponential function is given by, cothx…

Q: Find the rate of change.

A: Now the rate of change of given function is the derivative of given function with respect to x. So…

Q: arcsin = ab x² – Va² – y²; Find y'.

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Q: Match the expression in Column K (numbered) with its exact value in Column L (lettered).

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Q: 5] y=1+2x6 – 4x² – 2x6 - Standard Form: Degree: Sign of LC: as x→-0, y→ as x0, y→.

A: Solve the following

Q: いpO O siniz iff Z-kTi,K-o,っ3リーー Sin iz ニ

A: we have to prove that siniz=siniz¯ if and only if z=kπi, k∈ℤ.

Q: Use linear approximation, i.e. the tangent line, to approximate V125.1 as follows. Let f(x) = Vã and…

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Q: equation with the appropriate slope field. y' = x-y 11

A: Show slope field on graph

Q: 2y" + 3y' +y = +3 sint

A: To find the solution of given differential equation  by using the undetermined coefficient method…

Q: Exact Differe ntial Equation: x(3xy – 4y +6 kdx + (x² – 6x²y² -1\ty=0

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Q: Approximate 184 using the Linear Approximation L(x) of f(x) = x' at a = 16. (Use symbolic notation…

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Q: lve, using the method of variation of parameters: y/" + 4g/ sec 2.x

A: We will first find auxiliary equations and then find complementary solution to it.

Q: А. ELIMINAТЕ THE ARBITRARY CONSTANT/S IN THЕ EQUATION. 1. у%3D Ае2х + Вхе2х 2. у%3D Ах?+ Be-x 3.…

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Q: exact

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Q: Question 40

A: Algebraic method: First, get rid of the absolute value sign, then solve for x.

Q: Using Milne method obtain from the given table of tabulated values and y =y -x

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Q: | (56- x-x2) dx has its largest Find two numbers a and b with asb such that value. a a = and b =

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Q: %3D or False: If y=lne, then y'= 1? Explain

A: y=ln(e) => y = 1

Q: 6] y= 4x+2–- 5x6 Standard Form: Degree: Sign of LC: as x→-0, y → as x 0, y→

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Q: dy -1,-if x²+y?=9 then dx 1- 2- y 3-х-у 4- (x+y)/3 2-

A: The equation is given by x2+y2 = 9                                        .........1 To evaluate:…

Q: 5. Exact Differe ntial Equation: x(3xy-4y' +6dx+(x' -6x'y' -1dy = 0

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Q: @l1z.1-121151\2.-Zl By using:- Re(Z)sI ReCZ)l5|ZI V ZEC, Im (Z)<Imcz)

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Q: Date Page. QMle cylindaical coordinatu te evaluate and Jy x:18-14y-472 th x=2 and z>O

A: Solution is given below:

Q: Euler's diFFQ 3. Eqc) ((x) -24(x)=x(y しx1) ucx1-2uしx1 = x 1u(x) )

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Q: CV1-x² |1-x²-y² dxdydz Evaluate . /1-x²-y2-z*

A: Note down two integration formule which we use in calculation.

Q: Detirmine where

A: Given,             r→(t)=t2, 2t3, 1-t3

Q: acting on it by use of the component method. Show all your work and be sure to make a final…

A: component

Q: QI) Find and For F(x.y) = where x = y = .using a) Direct For F(x,y) = ar method by substitution x…

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Q: Differentiation [SND] If y = (r+ v1+x²)", prove that, (1+2²) 2 +ry - m²y =0

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Q: SV25-x² In dx , if we let u=/25 - x2 , then udu= - xdx. (A) True B False

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Q: S(sec z tan z – 3z²)dz -secz – z³ +c sec z + x³ + c sec - * +с tan z + 1³ + c O - sec z + z° +c

A: Use integration rules

Q: =x+6 Line 1: y= 2 Line 2: y=x-1 =-x LI

A: In system A, L1:y=x+6L2:y=-x The graph of the lines are intersect at one point. Hence there is…

Q: 1+iz : If w = Find the im age of z|<1. 1-iz

A: Let the transformation be f(z)=w, in which x-y plane is converted into u-v plane.  Where z=x+iy and…

Q: Using an appropriate substitution, i) Evaluate fx*(1-x)³ dx. ii) Show that dx = + In 2 . (x-1)3 8

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Q: 1. Find f(x, y) obeying = - sin(x)y and f(0, y) = }(y +2)². %3D %3D

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Y= (10x; + x, } (5x, + x}

A: Consider the given: Y=10x12+x235x1+x225Partially differentiate w.r.t.…

Q: Chioma was asked to find (18x + 3)(6x° + 3x)° dx using u-substitution. How should Chioma define u?…

A: ∫(18x2 + 3)(6x3 + 3x)6dx We have to use u-substitution for the above function. To solve this, u is…

Q: 21 y=-5x Degree: Sign of LC: as x→-0, y→

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Q: examire Ha Fonchion FX24)=x° -12Xy+g+8 For relahive extrema and sadlle Point

A: For extremum of function of two variables, we find fx , fy , fxx , fyy and fxy . Then put fx= 0 and…

Q: using the product rule, how do I find the derrivative of  h(x)=cosxsinx

A: According to the question, we have to find the derivative of the function hx=cosxsinx. The…

Q: tanh(x) = %3D ete

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Q: 8. Find 4x(x +1)dx by means of two methods: (a) Do the multiplication first, and then…

A: The given integral is ∫4x(x2+1)dx. We have to find the given integral by the given two methods and…

Q: inverse motrix fo fine -2-2Xンこ1 -X, +3X2 t5X, = -2 %3D %3D

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Q: Evaluate dx using appropriate substitution. Verify your answer by differentiating. an 1+ 2¤²

A: Given,           ∫x2x21+2x2dx