1) Let u = w² z³, where w = s?t, z = se-t. Find u when (s, t) = (1, –1).

Q: Let z= y- 4a, a u'v and y-v- 3u. Compute On kum)-(1,1) -

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Q: 16) Which function will shift y= vx right 4 units and up 1 unit? A) y = Vx + 4 +1 B) y = Vx + 1 C) y…

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Q: Given that f(r, y, 2) = }2 + }y – 322 – 5xyz. Calculate: (a) f.. (b) f., (c) f., (d) f.. Given that…

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Q: Solve for u(x, t): 1 3ux + 4u=0, u(x, 0) = 1 + x²

A: Given that the differential equation is:                             To find the solution of the…

Q: 1. (J · K) v (~ J. ~ K) / :. J = K

A: There are three expression in the given logical statement. They are J.K ~J.~K J≡K We prove the two…

Q: If f(r, v) = ry – ry", find 7 + ±),-.y-a

A: The power rule of differentiation states that d dxxp=pxp-1, where p is any real number. Use the…

Q: Let w = x? dx + y? z² dydz. Find dw.

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Q: Consider the exact U (x,y) that 2x + f = x taf Statistics. au aa au DDE (2x+ f) dx + (x + ² f) df =…

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Q: Let f= 2zy + yx, v= [y, z, 4z -x]. Find Dyf at (2,1,2). NOTE: Enter an exact answer. Dvf (2, 1, 2) =

A: Given: fx, y, z=2zy+yx, v=y, z, 4z-xTo find: The directional derivative, Dvf at 2, 1, 2

Q: et u = e Sin P= sin sc Lind su using chain Rule

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Q: O Find Vf, where f(x, y, z) = = e¯(ax+by+cz) with a, b, c some constants.

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Q: dz If z(x, y) = x²y, æ = 4, and y = u³ v², find du

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Q: 3) Express aw/ar and aw/as in terms of r and s if w = x +2y+z², x = 5, y = r² + Ins, z = 2r

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Q: Find (r.)ifr=√.e and r₁=(. In (21)) r, dt

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Q: Let f(z) = 5z2 + 3z.  Find u(x,y) if z = 8.2 + 5.9i

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Q: / (sec. sec u tan u -1) du

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Q: Q3: If z = f(u,v,t) = Z 3u? + v2 ,u = tet , v= te-2t Then dz at (2,2,0) at

A: Topic:- partial derivatives

Q: B) If f(x.y) x'y? +x*y , find: axdy *Əyər

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Q: Given f(x, y) = sin(x2) + xy³, find Duf(x, y) where u is in the direction of (1, 2). What is Duf(-2,…

A: To find the directional derivative of given by function

Q: Find y'(0) and y"(0) from the following table ofvalues: X 0 1 2 y 4 8 15 3 4 7 6 5 2

A: From the given table upper digits are values of X and lower digits are values of Y(X).

Q: The set of all linearly independent solutions of D.E yY-y 0 is Select one: a. (1,t,e',e ) b.…

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Q: Find J(u, v) if x = u + v, y = 2v.

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Q: Let f(x,y) = In (x³y). If fx(6,2)=fy(5,a) what is the value of a? а. 1 O b.-1 O C. 0 O d. 2 O e. -2

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Q: Assume w = ts³, 4ts) and (x,y) = 6xy of (х.у) - 4х Find as when t = s = 1 %3D

A: Given: From the given expression it is clear that 'f' is a function of 'x' and 'y', and 'x' and 'y'…

Q: where Dx = X₁-X₂ and Dy = |Y₁ — Y2]. Assume that the two locations are independent and uniformly…

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Q: If u = x²zî + yz?j – xyk and 0 = x²yz then find the value of u. (To)

A: Consider a function fx,y,z. The gradient of the function can be defined as, ∇→f=∂f∂xi^+∂f∂yj^+∂f∂zk^…

Q: 2: find fr, fy, and fz.

A: Given fx,y,z=e-xyz to find fx differentiate with respect to x fx=e-xyzyz

Q: 01. If w f(u, v), u = cosx and v = sinx, show that: d'w dx2 = v? fuu + u? frv - 2uvfur - ufu - vf,

A: Given w=f(u,v), u=cos x and v=sin xso we see that dudx=-sin x =-v   and dvdx=cos x=u.By chain rule,…

Q: Find aw in terms u and v if du w= In(x2+y2 +z²), x = ue" sin u, y = ue' cos u, z = ue"; (u, v) =…

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Q: dx and u = 3x-2 1. y 2+1 + 3

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Q: HW) If rCH)=6 sinzt ċ+ Gcas zt j + 5tk find F,Ñ, V, a and speed at t-2

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