2. [E2.1-Q33(a)] Show that the value of the determinant is independent of 0. sin 0 - cos 0 sin cos cos sin 0 sin cos 0 0 + 0 0 1

Q: dz (a) Find of the following functions: dx 2 zxa+!cos y? = sin(yº + 22z) where a - The first digit…

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Q: Let X Beta(a, B) andY Beta distribution pdf: fx (x) = caª-1(1 – x)8–1 for x E (0, 1) and parameters…

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Q: (r,1) = (r sin (f), r– cos (1)), (r.1) = (5,-) s numbers in exact form. Use symbolic notation and…

A: In this question, the concept of the Jacobian of functions is applied. The Jacobian of Gr,t is…

Q: c. sin"(t)- cos (t) = 2sin (t)-1 = CS d. cot (2y)+cos?(2y)+ sin (2y) = csc²(2y)

A: Given,  c. sin4(t)-cos4(t)=2sin2(t)-1d. cot2(2y)+cos2(2y)+sin2(2y)=csc2(2y)

Q: cos(z) = -1 %3D z%3D2пл + ilog.e (1 + /2), п € Z A z%3D (2n + 1)л,п € Z В z = z = (2n + 1),,n E Z z…

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Q: Find az/ax and dz/dy. xyz + cos(xy) - 2y sin(x) + z² = 3 Find az/ax and dz/dy. exz ZX y

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Q: 12) Based on below complex functions, what is W¹? W₂ 30y - 8 (Cos (4) + + sin (47)) 3 103 = 2 (cos…

A: we have given that  w1=8cos4π3+isin4π3w2=2cos7π3+isin7π3 then what is w1w=?

Q: on of y" – 2y' + 2y =

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Q: The solution of (e® + 2xy²) dx + (2 cos 2y + 2æ?y) dy is given by (A) e + x²y² + cos 2y = c (B) e+…

A: Answer:- The solution of ex+2xy2dx + 2cos 2y + 2x2ydy          —       (1)

Q: Example: Sketch the direction field for the equation y' = y – t over the square -2 < t, y < 2, then…

A: The direction field is a graph of small line segments passing through various points whose slope is…

Q: How to find the distance and midpoint between P and Q? P (-1,16) Q (5,-8)

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Q: 3. The points where r = 1 – cos 0 and r= cos 0 intersect are (A) (0,0) (B) (0,0) , (C) (0,0) (D) (E)…

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Q: ㅠ [sin(y) sin sin (y) sin² (y) 1+ cos(y) dy KIN

A: We will use substitution method to integrate.

Q: Suppose z=2– 3i, What is a complex function f (z) = – 37 – 2i Re (z) ? —6+ 13і -6- 13i об+13і 6–13i…

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Q: sin'a cos'a cos²x sin?x 1 1 10 12 2

A: We use properties of determinant

Q: Number 12

A: Hello. Since your question has multiple sub-parts, we will solve first three sub-parts for you. If…

Q: 19) For the ODE x(t) = e²t (c₁ cos(√3t) + c₂ sin(√3t) − sin (3t). cos (3t), let y = x' and 37 Y=…

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Q: sin(t) et, X2 sin(t)- cos (t) and X3 D sin(t) + cos (t)] 0. Given that X, cos(t) sin(t) + cos (t)|…

A: The problem is wrong, three vectors are not linearly independent.

Q: PDE: ) Solve the problem Ut = 16u1 BC: u(0, t)u(1,t) = 0 IC: u(x,0) = 2 sin(2x), u(x, t) = 0 0…

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Q: 5s Evaluate J|2 sin s Jdtds 0 0 I[ 2 OA. 3 (1 – sin(125)) O B. 3 (1+ sin(125)) (1+ cos(125)) 3 OC. 2…

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Q: Can you explain how all A B C D terms are calculated

A: Solution of the given question is like as

Q: Determina si las siguientes funciones son linealmente independientes fi(x) =x, f(x) = x – 5, f3(x) =…

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Q: I{e*sin 2t} =

A: Since you have asked multiple questions so as per our guidelines we will solve first question for…

Q: v (t) x w (t)=((t)i + (sin t)j + (cos t)k) x ((3t)i + 2k) ijk t sint cos t 3t 02 =(2 sin t)i + (3t…

A: The cross product of two vectors A and B is given by:A=ax i +ay j +az kB=bx i +by j +bz…

Q: b) Calculate the derivatives of y = = 3x² + 2 and y = cos x — sin x c) Calculate the integrals…

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Q: There are 5 boys and 4 girls. How many different ways are there to arrange these 9 persons in a row…

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Q: (1) Show that the function f(2)=z|z], where z=z+jy, is not analytic anywhere in the complex plane.

A: 1. The given function is fz=zz, where z=x+jy We have to show that fz is not analytic anywhere in the…

Q: 1. Use Cauchy- Reimann Equations to identify if it is differentiable or not, if yes then…

A: We have to find out that the given equation is differentiable or not and if it differentiable then…

Q: Use the method of Variation of Parameters to solve y" -y' = t.

A: The given differential equation y'''-y'=t. We have to the differential equation using the method of…