Q3) If f(x, y²) = x² + y² + vxy find af(x².y) and (x²y) ax ду

Q: Show that the equation Fu 1 u 0x² ² 3t² 0 is satisfied by u=f(x+ct) + F(x-ct) where fand F are…

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Q: f(x, y) = √5x² + 4y² fa(2, 1) =

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Q: then fxy Q4: If f (x, y,z) = x²y³ – y²z3 %3D -

A: we have to find partial derivative

Q: 2. F(x, у) %3D — (у i-2x) y2

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: ?w Əv у Find when u = 0, v=0 if w=x² + ₁ x=6u-2v + 1₁ y=u+4v - 1.

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Q: sVx? + 1d: Idx = 1

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Q: If f(x, y): X 2y + 1 use the definition to find af (x, y) ду

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Q: 13 |xsin xdx ーT 15 (xsin xdx

A: I=∫ x sinx dxIntegration by parts;u=x, v=sinxI=x∫sinx dx-∫(1 ∫sinx dx) dxI=-x cosx +∫cosx dxI=-xcosx…

Q: If then fyy = Select one: O True O False f(x, y) = 2(x² + x) (x - y)³ x² + y x - y

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Q: tet fz) =-iž, Showthat if z-iz,show thet if f(2) analyticcorno?

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Q: xy* Let f (x, y) = if (x, y) # (0,0) and f (0,0) = 0. (a4+6y8)

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Q: If f(x.y)= x?+2xy+5y² then дудх

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Q: Translate Q (0, -8) using (x, y) → (x - 3, y+ 2). Your answer: O Q'(-2, 5) Q' (3, - 10) O Q'(-3, -6)…

A: The transformation is, (x,y) ------> (x-3, y+2) So, (0, -8) ------> (0-3, -8+2)

Q: Differentiate: 3 a) F(y) = ( (y + 5y³) x²e* b) f (x) : x2+ex А c) f (x) : B+Cex

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Q: 13. In y = what is the derivative of 2x2 +3? x+1 a) 2x b) 4x c) 4x +3 d) 7

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Q: then If f(x,y)= x²y+ y, 3x O b. бху 6x O d. o

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Q: дz дz If z = f(x, y), find a and for the following equation əx ду z = x² + 3xy + y³

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Q: Find the differentiate

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Q: Verify that 5 18 11 2²4 ахду 22+ дуох - for f(x, y) = 2x³y6 - 4x5y4.

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Q: Find V x (V × F) if F(x, y, z) = 9xyj+ 5xyz k. V x (V × F)

A: Given function is F→x,y,z=9xyj^+5xyzk^. To find:  ∇×∇×F→ Concept: Cross product formula for given…

Q: For two points (x1, y1) and  (x2, y2) such that xi > 0, yi > 0 for i = 1, 2, we say  (x2,…

A: There are about 4 functions provided.To show:They are Schur convex or not.Concept used:i) Any…

Q: If z varies direct to the square of y and y varies inverse to x (x,y,x) = (20,120,100) Then find the…

A: z varies directly to the square of y, so z=my2 y varies inversely to x, so, y=nx Therefore,…

Q: If B = x°ya, + (2x + y)a, – (y – 2)a, find (a) V B (b) V X B (c) V (V B) (d) V x V X B

A: Given : B=x2yax +(2x2+y)ay - (y-z)az

Q: Find f if ∇f = 4xy i + (2x^2 + 8y) j

A: Here I am attaching image so that you understand each and every step.

Q: Q/ Let X be the r.v such that E(X) = 2, E(X²)= 2a , E((2+aX)²) = 2a3 Find the value of a. %3D %3D

A: Let X be the random variable such that, E(X)=2, E(X2)=2a, E((2+aX)2)=2a3

Q: If f(x, y, z)=√x²y² z², then fxyz (x, y, z) = 2xyz √x² 1² z² Select one: True O False

A: Given: if fx,y,z=x2y2z2 then fxyzx,y,z=2xyzx2y2z2 We have to state if the given statement is true or…

Q: Find the value of fr and fy at (1,-1) when 4 +5x² + 3y². xy f(x, y) =

A: Given: fx,y=4xy+5x2+3y2We need to find fx and fy at 1,-1.

Q: af ду 5z + 14y If f(1, y) = is : then 5z — 14у 140z (5z – 14y)? 140z (5z + 14y)2 140z (5x + 14y)2…

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