Find d2u/dv2 given that: u = 28v + v4 – 9/2v

Q: By using the substitution u = 4x +1, evaluate (4x + 1) dx %3D

A:

Q: (b) Find dy

A: Given that: exy+x2-y2=10

Q: Find r'(t) r(t) = 6Vti + t²Vtj + In(t? )k %3D r'(t) = %3D

A:

Q: Find V x² +y dædy, where A{(x, y) E R; ² + y < a?}

A:

Q: Find a suitable A and B so that: A < S, Vx+4 dx < B

A: The given integral is ∫29x+4dx First evaluate the integral as follows.…

Q: dy Use separation of variables to find the general solution to dr + 4xy? = 0. %3D

A: We have to sine given differential equation using seperation of variables

Q: If WZ = 68 and UV = 94, what is XY? %3D V W Y U Z

A: Given ,  WZ = 68 , UV = 94  We have to find XY

Q: Find V (V x F), if F(r, y, z) = 7e""i + 2xe"j- 3e""k.

A:

Q: (c) S, y*/1- y² dy

A:

Q: » / 13t – 41º + 4 dt = 6. (а) 1 - 5 Jū du: (b) dx = 4x3 (c)

A:

Q: What is the point on y = 2 Vx that is nearest to (4, 0) ? A) (2 V7.27) B) (2, 2 Vz) C) 2/6 3 D)

A:

Q: 8. Let D be the rectangle given by -1<ys0, 1s x< 3. calculate ff,(x2 + y)dydx

A: 8. We will evaluate the given double integral. Given integral is ∬D(x2+y)dy dx with the limits…

Q: 4. The square STUV has diagonals that intersect at point W, where SU = 4x + 26 and TW = 8x- 41. Find…

A:

Q: Solve : dy- (- y) . Inn dy %3D ,13-1 Ordinery Dibberential equetion.

A: Solution:Givendydx=(1-y13)x2 ln xy13-1

Q: Find mZB. C 10 10 D mZB %3D Submit

A:

Q: Find mZG. E 35-/2 F 70/2 mZG %3D Submit

A:

Q: EX:- Show that dw Vす 2. の ē" dw fcb)-VEerfa) %3D e dw ei

A: Using error function erf(f) .

Q: Sll, dxdydz , where T: 0 < x < 1, 0 < y< v1 – x², Vx² + y² < z< /2 – x² – y²

A: we have to triple integrate using the given limits

Q: Given that y = dx dy 3u?, : 5v² and v = 2x2. U = 8. Find

A:

Q: dp For p(q).= q¯³, dq -3 dw For w(u) = u7, du %3D %3D

A:

Q: dw -is equal to: dv If w = 5u, then 5w5 v(1 – 20u In v) 5w v(1 – 20w5 In v)

A: Given, w= v5w⁴ To find, dw/dv

Q: B (2x + 3y² +42³) dV, where B = {(x, y, z)|0 ≤ x ≤ 1,0 ≤ y ≤ 2,0 ≤ #≤ 3} 08 192 170

A: dv = dxdydz And put the limit of integration.

Q: Differentiate. V(t) = (t + 7e')/t %3D 3 7/)eIn(e) + v7 * V'(t) = 2

A:

Q: dz, C:z| = n. %3D 2++13z2+36

A:

Q: S(2y + 3)?/ y+ 2 dy

A:

Q: Q3:A/ Find: dy dy y 2 Vy (1 + Vý)² yV4y? – 1 |

A:

Q: 2. у"dy 3D х (хау — уах)еу 3. ydx %3D х + Vу? — х?dy 2 (1n In v) d, - y (1ulny ulnr) di

A:

Q: Solve the PDE to find Z AZx + BZ, + CZ = 0 %3D where, Z(0, y) = e3y %3D

A:

Q: - show that; L-1[e¬v$] = e %3D 2tynt

A:

Q: t2 d?y dt2 4t + 6y = t3 + 1 + 6y = t³ + 1 dt

A: Differential equation

Q: ) find "c" s.t P(S² < c) = 0.95 if X{:n(µ, 12),n = 6, X² = 11.10. %3D

A:

Q: Find V · (V × F), if F(x, y, z) = 6e²*i+ 5xe"j – 2ev³k. %3D -

A:

Q: Find mZT SU. S U 26° T

A: Solve the following

Q: (x, v) = (2ry) i + (r – 2rv) j ,2]. -

A:

Q: Sx 5x * rysin(z* + g*)dzdy Find 0.

A: Given:

Q: Supposo that | FC) dx =13, fい)n -23, and gla)dx=35 2. fCx) drx = こxp(の J3fa) dx= C+fし),33J- 2.

A:

Q: find dy,if y= x²+2)Cx*+3x+) %3D

A:

Q: Utt = v²u и (х, у, 0) — 0 k constant ,u (x, y, t) = k

A:

Q: u³ = a²t , find d’u %3D dt3 2a4 а. 9u5 10a6 27u8 -10a6 С. Zu® 40a6 d. U8 b.

A: A detailed solution is given below

Q: 5) *=ClSln t ,y =4 csst t=-2 %3D a) determine dy b) and graeh

A: we have to find derivative

Q: In the diagram below we have that ST B = 69° and CDU = 62°. %3D %3D E A S -V U Find: 1. ВСТ 2. ABT =…

A:

Q: dt if t = (8r' +2r² +3) and w = dw =(r* +2)*. Determine

A: Derivative

Q: Solve the IVP y" + 4y/ + 5y = 38,(t), y(0) = 0, y'(0) = 1. %3D %3D

A:

Q: Evaluate SSS9e=+y²+=?)** dV over B where B = {(x, y, 2) : a? + y? + z? < 1}. Take = 3.

A:

Q: differentiate. a) g(t)こ3-2t St +1 c) H(u)= (u-JJ) (utro) d) FLt)- モ-3 %3D

A:

Q: Find V · (V × F), if F(x, y, z) = e2²i+ 7xe'j – 2e²k. - V·(V × F) =

A: Solved below

Q: Q2: Given y = f (u) and u g(x), find dy/dx: y = 2u3, и %3D 8х — 1

A: Differentiate

Q: Find S- y dy Vy+2 using the substitution u +5=√√y+2.

A:

Q: Find V· (V × F), if F(x, y, z) = e®²i+ 4xe®j – 5eV²k. V.(V × F) =

A: