1. 2r +3y 5 at (1,1)
Q: 4. dr/dt = -2tr, r(0) = ro %3D
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Q: find ƒx , ƒy , and ƒz . ƒ(x, y, z) = 1 + xy2 - 2z2
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Q: 4. If u = xy + y²z³, where x = rset, y = rs²e when r = 2, s = 1,t = 0.
A: We have to find solution
Q: Suppose that f(æ, y) = e" = e-3z? - 4y? +y
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Q: (11) Evaluate [[3x+5y+i(x²-y') dz along y=x (0,0)
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Q: Evaluate ſſs 3y dS where S is the portion of y^2 + z^2 = 4 between x = 3 and x = 3 - z. %3D
A: The surface is ∬S 3y dS=∬S1 3y dS+∬S2 3y dS + ∬S3 3y dS
Q: Let z 2ev Then: 8z 8z dy sissis
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Q: If it is known that L {y'' (t)} = -15s+24 with y(0) = -3 and y'(0) = 6, then it can be ensured that:
A: The given problem is to find the Laplace of y(t) from given info, given Laplace of y"(t) =-15s+24…
Q: 6. +4y> S 7. 15m+42s 8. pe-5 9. 52x+y 10. -zy-3r +S ame Cortesian anc
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Q: 3+2s 17. F(s) %3D (s+4)(s²–3)
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Q: 1.) Evaluate: S(2 + y²)²dy
A: We have to find integral
Q: Evaluate dz where ci) .C is 1z+ Yzl =2 Ci) c is 1ztil=1
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Q: 26. у" + 4y' %3D sec 2x
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Q: Evaluate S S"(2y² + x)dædy
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Q: 4[8,(t-2) rect(r)dt
A: we have, I=4∫020δ4t-2recttdt we know that ∫t1t2xtδt-t0dt=xt0 ; t1<t0<t20 ;…
Q: 15. In AXYZ, XY YZ and m/XYZ = 46*. %3D 46
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Q: 1. If (x and jy) = 3 + j8, find x and y. x = 2.40 and y = 1.67
A: According to policy we are allowed to do one question. Image is attached with solution.
Q: for w = ze(zy²+2:). Do not include =" in your answer.
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Q: 2) Show that (1 – x²)P",(x)P'm(x) dx: 21(l + 1) Sim• 21 + 1
A: Given:- ∫-11(1-x2) p'l(x)p'm(x)dx=2l(l+1)2l+1δlm
Q: (8) If w = 5x2 + 2y2, x -3s +t, and y s - 4t. %3D aw and at aw Find as
A: w=5x2+2y2, x=-3s+t, y=s-4t
Q: Use the fact that 9(z) dz 65 to compute each of the following: g(y) dy = %3! | 9(z) dz 9(z) dz %3|…
A: We use definite integral properties
Q: * In z dz = 1 A 25 4eb+1 25 B
A: Given:∫1ex4lnx dx
Q: 9. If x2-xy + y2 = 3, find y' and y", %3D
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Q: If x2 + y2 = 2st − 10 and 2xy = s2 − t2, find ∂x/∂s, ∂x/∂t, ∂y/∂s, ∂y/∂t at(x, y, s, t) = (4, 2, 5,…
A: If x2+ y2 = 2st − 10 and 2xy = s2 − t2,To find∂x∂s,∂x∂t,∂y∂s,∂y∂t at (x, y, s, t) = (4, 2, 5, 3).
Q: .1//3 7earctan(y) dy + y? 3
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Q: 3. If 4=(x+2y+az,bx– 3y-z,4x+cy +2=) is irrotational. Find constant a,b,c.
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Q: 3. If z* +x²z+z+y = 0 find (1) Əz/ax, (2) əz/əy, (3) ²z/dx², (4) d²z/@y², (5) Fz/dxəy, and (6)…
A: As per our guidelines, I am only solving the first three. For other kindly upload the question…
Q: 2こx+iy 2 Recz) =l 3-i1 if 121 =2, then
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Q: If x + y + z = 12 & x² + y² + z² = 96 & !.!,!= 36 then value -+-+ -%3D X y of x³ + y3 + z³ is
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Q: EXAMPLE 4: WY = In AWXY: WX = 9 m, XY = 15 m, and n ZW =31° m2X = mZY =
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Q: 3. (z, y)(1.5x, 1.5y) A' will be located at ( B' will be located at ( C' will be located at (
A: We have given the scalar factor i.e . (x,y)=(1.5x,1.5y)
Q: 3-VE For dz, z = 2+vz
A: Given, ∫3-z2+zdz
Q: B) fometie w= xty+y2-23, x²ry*+2?=6
A: Note: Since you have asked multiple questions, we will solve the first question for you. If you want…
Q: 4. y=6-ax-x", y = x+l6, about the a %3D | yaxis
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Q: 2. f(x,y) = x5 In(y)
A: Given function is fx,y=x5lny. To find the first and second order partial derivative of the given…
Q: O y'+ (oy -asin 8t y W): -1 2
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Q: d's 36cos(6t + T), s'(0) = 200, s(0) = 0 .2 dt
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Q: If s = 4/t - 3, then %3D ds dt
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Q: (,² + 4y² )0.5_x = se!y =r!0in(r) find Ou 2 0.5 when s= 2, r = 4,t = -3
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Q: j. Min Z = 12x, + 8x, subject to: 4x, + 2x, 2 24 2x, + 2x, 2 10 2x, < 8 X,, X2 20
A: To solve the Linear programming problem using the graphical method Consider the constraints as…
Q: 2 dt t² +2t +3 18. Evaluate 8 dz z² +8z+ 25 20. Evaluate o
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Q: لله √ √³ √ √² zysin(2² + y²) dz dy −
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Q: 2. § (5z² - 7z + 3) dz from z = 2 to z = 1
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Q: Find the antiderivative of: dt/(1-7t)^3 where u = 1-7t
A: To find antiderivative
Q: 3. If (x, y, z) = xy²z find grad 6 at (2,−1,3).
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Q: 3. Find and at (0,0) where if (r, y) # (0,0) if (z, y) = (0,0) f(1, y) = Are they equal?
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Q: 39. If z = 5x² + y² and (x, y) changes from (1, 2) to (1.05, 2.1), compare the values of Az and dz.
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Q: 2/3 If y = xl/3 + 2 dy then |z */0 =-8 dr
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Q: 2s+2 ds = In|s| – In\s + 2| + C %3D s3 +3s2+2s
A: Here, we are solving only 1st question and for the remaining question post the question again.…
Q: 6 4 for f(x, y) 3 3x у - 4x'у". 5 3 Verify that дх ду ду дх df 4 5 18y x - 20y°x of 5 3 4. 2 18x°y -…
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- a) y=(x+2)/x^2 - 1) b) y= ((x^2 - 1)(x+2))/ x-3 find the x and y intercept, symmetry, region/scope, asymptotes, critical points, point of inflection, and sketch the curve of the two givenAn equation of the line tangent to the graph of g at x = 3 isy = 5x + 4. Find g(3) and g′(3).(a) If the function f(x)= x^3+ax^2+bx has the local minimum value -2/9 cube root 9 at x= 1/cube root , what are the values of a and b? (b) Which of the tangent line to the curve in part (a) has the smallest slope?
- a. Let y=f(x) be the particular solution to the given differnetial equation with the initial condition f(2)=1. Write an equation for the line tangent to the graph of y=f(x) at x=2. Use your equation to approximate f(2.1). b. Find the particular solution to the given differnetial equation with the initial condition of f(2)=1.Two towns A and B are 5 km and 7 km, respectively, from a railroad line. The points C and D nearest to A and B are 6 km apart. Where should a station be located to minimize the length of the new road from A to S to B? (grade 12 calculus, use derivatives)the ideas presented in this section, what do you think is thearea under the curve of y = 2- x bounded from below bythe x-axis and on the left by x = - 4? Justify your answer.