a2 Q2. If a¡j = aji are constant, calculate (aijX;X¡) axkəxi

Q: re with a constant electric current, if there is heat exchange between surface and the surrounding…

A: Sol

Q: given f (z) = 32² – 6z + j3, what is the value of u(3, 2)

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Q: 2. s - [GpAq)Ar] = a. 7 [(pV7 (qAr)) As] b. (pV7 (qAr)) As с. (pV (qAr)) d. None of these

A: The given question has been solved with explanation in step 2.

Q: dt, then for a2 0,ƒ 9. If f(7) = J. Je +1

A: We have to find the derivative of the function.

Q: 2.Evaluate . xy+ds where C is the right half of x2 + y? = 16

A: Integrate with use parametric form

Q: Q.1B) If w = f(u,v) where u = tan"12 &v=In(x² + y²), the show that: dw Х- +- дх дw dw <-2- ду ду

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: Find the values of the constants a, b, c so that F = (axy + bz*)i+ (3x² – cz)j + (3xz? – y)k Is…

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Q: Q3) If f(x, y") = x + y? + Vãy find: af(x²y) and Ty) ду afxy)

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Q: H In OJ, GH = 9, KL = 4x + 1. Find x. R 5. 5 S. GK

A: Given: GH=9,KL=4x+1  If from a centre a perpendicular is drawn to the chord, then a chord is divided…

Q: 7. For what values of m does the function y = e™* satisfying the following equation y" – 3y' – 10y =…

A: We have to find the values of m.

Q: Q3 Evaluate fII, xyz dxdydz, 3 < x < -2,0 < y < 1,0 < z S.

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Q: dt 20.5 t2+2t A - In|t? + 2t| + C B. 2ln +C C. In +C D. In + C

A: First we common out t2 from denominator and then put 1+2/t=u and differentiate both sides with…

Q: Consider the problem min 12 s. t. 1+ r2| <1, IEX R.

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Q: 3 If f(t) =e3t , then L{f (t)} s-t ulgn ihi

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Q: EX: Verify that z= I+ V3i satis fies the 2. eq.

A: the given equation is z2-z+1=0 given the value of z is z=1+3i2 substitute the value of z in the…

Q: Calculate (aijkXiXjXx), where the a¡jk are constants. axi

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Q: (3) State whether the following statements are true or false and justify your answers. (a) 3x E Z 3y…

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Q: A- If y = e3x and y = e-3x , prove that: - d²y dx2 – 9y = 0

A: The solution for the above question is as shown below.

Q: How do I prove this?

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Q: b) (i) Show that dz is a constant independent of z, and R. { Hint : z= Z, + Re"} 1 +- 2z-4 2 -z 3…

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Q: Given ay" + by' + cy = f(t) where a, b, and c are constants. The response is overdamped if b^2 - 4ac…

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Q: Find the values of the constants a, b, c so that F = (axy + bz3)i+ (3x² – cz)j + (3xz? – y)k Is…

A: A vector F→ is said to be irrational if and only if cure F→ =0 i.e∆ x F→ = 0Given F→ = (axy+bz3) i^…

Q: Q3) If f(x, y²) = x² + y? + Vxy find : af (x?y) and L(x?y) ду ax

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Q: Q3: van fy = xy*-1 + x",In(x) f(x,y) = x +y* • if it was True false

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Q: Suppose that a?y +xz? = 3 and let u = -r³. Find the value of du when (x, y, z) = (1, –1,2). dz A) –2…

A: Given that: x2y + xz2= 3 and u=-x3 and (x,y,z)=(1,-1,2). We find du/dz ot differential with respect…

Q: Let X ~ NB(r, p). Show that E(X*) =-E(Y – 1)*-1 where Y ~ NB(r+1, p). а. b. Use this result to find…

A: It is given that:

Q: Let z=xin(x2+y2-e4)-176xy, x=te, y=est, If the value of z when s=2 and t=1 is equal to Ae?+Be4, then…

A: Explanation of the answer is as follows

Q: If u = a − j20 and v = 6+ jb, calculate the value of Im (1).

A:

Q: If u = ₁+₂y+z, where a₁, A2, A3 al constants and J²u J²u J²u น a +a+a = 1. Show that + + = U. მ2 მყ2…

A: This question is based on Partial diffrentiation.

Q: 3 - If h(x, y) = y – xy – x2, find at the point (2, n) ду

A: The given function is hx, y=y-xy-x2 and the point is 2, π.

Q: Let x be a c.r.v., the E(x4) can be founded by xf(x) dx. O True False

A: Given problem Given that   Let x be a c.r.v., the E( x4 ) can be bounded by ∫-∞∞xf(x) dx   Ans)…

Q: Find x E R that satisfies -2 , – 02 + 2 vz U2 det = x det + – ö4 2 0 + 03 U3

A: The key concept to solve the given problem is that : The determinant of a matrix remains unchanged…

Q: dt Determine dw if t = (6r* +3r*) -(*+2r-5)'. -s)'. and w =

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Q: hnd the linear apprakimation ot x:0 to t6-x Weite ny.Ax-b answer in

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Q: Q: If u =f(x² +2yz, y² + 2=x)Prove that (y-ax

A: Step by step compute the derivative with respect to each variable x,y or z. Then substitute it in…

Q: Let f(x, y) = ax? + by? – 16x + 30y + 14. If the point (2, –5) is the only critical point, find the…

A: Given:      f(x,y) = ax2 + by2 - 16x + 30y + 14      The critical point (2 , -5)    The partial…

Q: Q9. If W = f(u)=u' + sinu+Inu, and a=ax+by, where a, and b are constants, show that aw aw b. ax

A: We have to prove the given statement.

Q: Find the solution of x = X₂ JED -6 where u(t) = 2 and x(0) = [1 -1]. 11 0 JUCE + u(t) (10)

A: The problem is solved using the concept of eigen value and eigen vector.

Q: Let z=xln(x2+y2-e4)-161xy, x=te, y=est. If the value of 2 when s=2 and t=1 is equal to Ae2+Be“, then…

A: From the chain rule, ∂z∂t=∂z∂x×∂x∂t+∂z∂y×∂y∂t Now,…

Q: Q3) If f (x, y²) = x² + y² + Vxy find : af(x².y) and f(x?y) ду ax

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Q: Answer the following True or False. dt sec 't |', \_ 1 = 27. |t|VE2 - 1 O True O False

A: sec-11=0 and sec-1(-1)=π

Q: -v-S vdu G) - S -r lee) dx 2 (보라2) 2 (x²t2) - x2 2 (R?+2) ㅜ 2 (x? qz) - (x? $2) z (? t2) In Ix? tz…

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Q: dw 22. If w = f(ax + by), show that b = 0. a ду Hint: Let ax + by = z.

A: Consider the following equation: z=ax+by Differentiate z with respect to x taking y as constant:…

Q: z=xln(x2+y2−e4)−176xy, x=tes, y=est.  If the value of    ∂z ∂t   when  s=2 and t=1  is equal to…

A: we have to partial derivative by using chain rule

Q: If C is given by x(t)=t,y(t)=t,0sts1, then S. | t?dt. xyds = Select one: True False

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Q: If T:R(T) - D(T) then T(x) =X@J T(x) =YoD

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

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Q: Q3) If f(x, y?) = x² + y2 + Vxy find : af(x²,y) and f(x?,y) ду

A: