30z2 – 23z + 5 Evaluate J (2z – 1)²(3z – 1) dz, C : |2| = 1 (counterclockwise). |

Q: f(x, y) = x²y + 4y and x = st, y = 2t - 3s. af and off. af Use Chain Rule to find ds Write your…

A: Follow the procedure given below.

Q: Evaluabe Is f" (2Z43) dz 1-2i Ans 17+19i a. directly lo, along the path x=2t+1, Y= 4t-t-2 C. along…

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Q: In Exercises 29–31, find the equation of the line tangent to thesurface at the given point P and in…

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Q: Q.4 Use the one sided Greens function to solve the I.VP. 1 12y"-6y=nt, 6 (0)=1/² y'(1) = y(1)=-

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

Q: x1, x2, x3...... x20000 iid U(2, 9), find approximation for 2X-20

A: Central Limit Theorem : If X1, X2 ..... Xn are iid random variable with mean μ and Variance σ2 then,…

Q: 8. The distance between the planes 2r-y-2z 5 and 2r – y - 2z = 7 is A C 2 9 dn 24

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Q: Q.6 Show that: X-1 X+ y – 1(x-1y)= B(x,y)

A: In the given problem we have to show that                                 x-1x+y-1β(x-1,y)=β(x,y)

Q: Q-VII) 2r +y+=3 Use Cramer's rule to compute the solutions of the following system: 2-y--0 +2y+ 0

A: The given system of equation is 2x+y+z=3x-y-z=0x+2y+z=0

Q: 3(x + 2)\/1 (x+2)² Which of the following is *+2) + arcsin 9 +C equal to? arcsin (z + 2) + (x + 2)v5…

A: Given that,     92arcsinx+22+3x+21-x+2292+C

Q: (b) Use Gaussian elimination to find the values of x, y and z: x+2y+3z=10 -x+y+z=0 y=z=1

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Q: The Power Chain Rule simplifies computing the derivative of a powerof an expression

A: To find the derivative of a power of an expression using the chain rule. ddxe3x+1 Solution: Chain…

Q: x-(1+iy) Q11: Express- in terms of z and z. (x-1)2+y2

A: Let z=x+iy and z bar =x-iy

Q: 4. (a) If y = A + Bx + Cx2 and yo, yı, y2 are the values of y corresponding to x = a, a + h, a + 2h…

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Q: Q2. (a) Show that {e=²,xe¯²} is a fundamental set of solutions of y" + 2y' + y = 0 (0, 0). on

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Q: (1) こ Wy2,y2)= 12 enx (2) 9/2 X 9) Y=(x)=e

A: It is given that the differential equation y"+3y'+y=0. Wronskian W(y1,y2)=12enx            ......…

Q: 2. W =I+xy- Z finds Wzz WZX NJ 3.

A: Given W = 1 + xy2 - z2

Q: 1 dz, C:k – 3i] = 3 z² +4z + 13

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: use Gaussian Jordan 2メ+4y+ 6Z = 18 4x+ Sy + 6Z = 24 3x + Y -2Z =4 thy answer should be like this:…

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Q: If f(1, y, 2) = In(z³ + y8 + z³) + V(z³ + y³ + z³), then find fr, fy and fa at (1, 1, 1).

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Q: T (k+m+1) k! I' (m-k+1) \x+1, P² (x) = m k/2 X ₂F₁ 2F₁ ( -m, m+1; k+1; +¹; 1 - - - 2 ) 2

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Q: f(z) = 2(x – 5)² + 3. - f (x) is invertible for which values of x?

A: Given function is: fx=2x-52+3 Then we get,…

Q: Determne y (8x +3)/2 from (11)/2 s ys (27)2?

A: Given: y=(8x+3)32     from 1132≤ y≤2732

Q: 1 of f(z): is z2+2z+2 %3D

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Q: 10 Let y = ( 2x + Then -A(2x + 10)" (2- 10)°, dy = A[ 2x + 2 - where A = %3D C = %3D

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Q: -3 and y = 2 0 Let x = ||x - y||₁ ||x - yl|oo = ||x - y||2₂ = 3. Compute

A: Given : x=-5-32    , y=330

Q: f(t) = e3t + cos(6t) – est cos(6t) As4 + Bs3 + Cs² + Ds + E F(s) Fs5 + Gs4 + Hs3 + Is² + Js + K

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Q: Given: xIn y + y²z + z² = 8 Find: дх дz -(x + 2y² z) y(y² + 2z) -y ln y x + 2y² z - In y у2 + 2z -у²…

A: Let's find derivative of given function.

Q: Find curl (3z i + 4x j + 7y k). curl(3z i + 4x j + 7y k) = ( i Di + ( i Oj + ( )k

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Q: ( b) For n=1,2,K , show that (x² –1)y"*) +2(nx + p)y") +(n² –n)y"-1) =0 where %3D d" y p") = (Hint:…

A: * Given that y = x+1x-1pa dydx = px+1x-1p-1ddxx+1x-1    dydx = px+1x-1p-1x-11-x+1.1x-12   dydx =…

Q: 4. Solve the equation T2T satisfying the conditions: at ax (i) T=0 when x= 0 and 1 for all t 2x,…

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

Q: z = 2 24 z=Vx² + y² 2 FIGURE 9

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Q: Q4: Let z = 2x² – y2 . Find all points at which |Vz| = 4. Then find V|Vz| at the point (1,4).

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Q: -E- x2 and S: R2 → R², 4. Let T : R² → R², x-y (a) Find (SoT)(u) where u := E R?. (b) Find a…

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Q: R X 1 Zィ Xieg ww v. Ex. R. Z.s V, Rieg+ Zis' (Rieg+ Zis)?+X1e3 =? %3D 2 + G0,s' - 229200…

A: We have to explain the calculations done in the image.

Q: (D^5-3D^4+8D^3+16D^2-9D-13)y=0 nonhomogeneous undetermined coefficients

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Q: 2 sec 0 r drde = x² + y² dydx %3D 0. True False Reset Selection

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Q: Мaximize p = 10x + 10y + 15z subject to + z s 12 X y - 2x 2y + z 2 14 -y + z 2 4 x 2 0, y 2 0, z 2…

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Q: f(z) = 3z + 8z² - 72 - 4 g(z) = 27 – 6 Find (f- g)(x). O A. (f - g)(x) = 3r + 8z2 – 5x – 10 O B. (f…

A: Simply substrate algebraically the similar terms only.

Q: Q3: Find the value of n which F(x, y, z) = (x +y +z*)" to satisfy fxx +fyy+ fz= 0. 1

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Q: QY Use Gramer's Rule to Find K,y and Z -y-22 =-8 %3D 1 + 32 = 2 %3D 7X +y+Z = o

A: Craners rule used

Q: 2z - z 3 Prove that if z E C and |2| = 3, then %3D 3i + z2 21 VI VI 1/4

A: Given that z∈ℂ and |z|=3. To prove-14≤2z-z¯3i+z2≤32                 ......(I) Recall that, z1-z2 ≤…

Q: | 2.xdV where E = {(x, y, z) |0 < y < 2, 0sxs 4- y²,0<z< y}

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Q: 11 f(x,y) 3x-7y+2, R is the rectangle with opposite car- ners (-1,0) and (1,3).

A: 12. Given: fx,y=2x+2y+2 and triangle with corner 0,0 To find the area of the triangle. The formula…

Q: b) y = -x -1 -u) 4 = 3x +5 -ài) a) 2x +3 %3D y = 4x -) -ài, Bub ci) from il cis from ei) Sub = 4n -…

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Q: (a) The function z depends on u and v so that z = 2v(4- 3u)? u = 2x + 3y and v= 3x-2y az when x 0…

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Q: Suppose that r, y, z satisfy the equations x+y+z = 5-a %3D 2x +y = 7 – a %3D x - y – 2z = 0, %3D…

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Q: 2: find fr, fy, and fz. 9 f(x, y, z) = 1 + xy? - 222 5 f(x, y, z) = x - Vy² + z?

A: (a) Given f(x, y, z) = 1 + xy2 - 2z2 So fx = ddx(1 + xy2 - 2z2)    = ddx(1) + ddx(xy2) - ddx(2z2)…

Q: 6x + 6 13 dx Evaluate - x4 -3 О З2? + 2 - 13x + C, Where C is the parameter O 3x2 – 2 3 – 13x + C,…

A: We have to find

Q: 2. 2 +3+5t t(2n-1)=h(2n-1s (2nt) %3D 3. for all nz I

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.