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Q: Define Lagrange Identity?

A:

Q: 8. JOLvate using Using res idue theorem -00

A: Given: ∫-∞∞x2dxx2+1x2+4

Q: Prove fulay's formule -CstD)4isin LO)

A:

Q: Find Souution of ODE xy"+y't x²y 20

A: Given, the differential equation                  xy''+y'+x2y=0                 ...(1)

Q: Suestane what be Scrd abaut the senes? con from the limid Comporson test 2) le 6) None we convege c)…

A:

Q: Verify that He follow egunbin is an ielartiky Fan o -sino 2 tano

A: We will use various trigonometric formulas to answer this

Q: be sec of SIze an B SiZe HOW mons funce ions f:A B are there chas for every beB, there eleme n Es…

A: Given that the size of set A is  8 and size of set B is 4. Now to be total number of functions f:A→B…

Q: Poove the destity following

A:

Q: 7. There are two lifeguard stations along the shoreline. Station B is 50 meters east of station A. A…

A: First, draw a figure according to the question, the figure is a triangle. Then by applying the law…

Q: a420Provetthat the fortiaof22)+719tz) 5atsaContintontat

A:

Q: prove that the covariant derivate satisfies leibniz's rule

A: The main reason behind the covariant derivative satisfying Leibniz's rule is it maintains chain rule…

Q: Hoist meihanism with a colera tion finu dis Plucement *こV1+o.256 ;PVニomis Sz3m for もこos and…

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Q: Prove that the identity is true.

A: Given a). b).

Q: ( ग০) (১০ for the following func tion ? -WX-+5inZっメー +SinZっメー

A: w=x2+y2-z+sin zx+y=z(∂w∂y)x =ddy(x2+y2-(x+y)+sin(x+y))            =[0+2y-1+cos(x+y)(0+1)](∂w∂y)x…

Q: 2, 2. prove that tan¯0+cot-0+2= sec´0cosec´0

A:

Q: +x +13 2x + 2 What is the value for x? O 10 O 11 O 5

A:

Q: Show that if Y = ax + b (a = 0), then Corr(X, Y) = +1 or -1. We know Cov(X, Y) = Cov x, ])--)-I + b…

A: We need to show that, If Y=aX+b then Corr(X,Y)= +1 or -1

Q: 1\\nDetermine all values between 0\\\\deg and 360\\\\deg that satisfy the following expression:\\n…

A: The objective of this question is to find all the angles between 0 and 360 degrees for which the…

Q: csce csce + = 2 sec? 0 Csce — 1 'csсө + 1

A:

Q: 5) Find the following of the function f(x,y) =xy+cos y+ysin x

A: To find: The partial derivatives ∂2f∂x2,∂2f∂y2,∂2f∂x∂y. Given: The function is fx,y=x2y+cosy+ysinx.…

Q: Prove that : <(tan"e) - Ve +1 2e 2 +. Ve? +1 tan

A:

Q: Prove that f, uv v • dỉ = – §̟ vũu • dĩ

A: Whenever the force is conservative in nature the work done over the closed loop is always zero. i.e…

Q: Prove tuat fsecodo-On/sece + tanco

A:

Q: 5: Is the following tmchan diHenentiable. ) frem = ? í) fle) = 121* %3D (리 i) f12) - Sin? Cos 2 v) t…

A: According to guidelines we solve only first three parts.

Q: tanx cotx = cscx secx

A: Given the identity: The aim to prove the identity Trigonometry Formulas:

Q: Prove that x² = 13 (1²) + 1) = (xin(e))) ১0 sin(0)

A: Given  x=rsinθ cosϕy=rsinθsinϕz=rcosθ To prove :∇2=1r2∂∂rr2∂∂r+1r2sinθ∂∂θsinθ∂∂θ+1r2sin2ϕ∂2∂ϕ2

Q: 1+ cot2 0 cot? 0 - sec² 0.

A: Given, 1+cot2θcot2θ we have the relationship  1 +cot2θ = csc2θ    ..............(1) and cot2θ  =…

Q: To prove L'Hopital's Rule for the case, you use what Theorem and what statement is a direct result…

A: For ∞∞ case, we can use the l'Hospital rule by taking the derivatives of numerator and denominator…

Q: 7- drotan G) Find des dy

A: Given a function : z=arctanxy We need to find dzdy.

Q: (b) Prove or disprove that det (ABCD= det(A)det is jaett Jaet(D)

A: Let A=1111,B=1221,C=1332,D=1212 Therefore the determinants of individual matrices are: A=0,B=-3,C=-7…

Q: H012.3.4,53 Find sets CandD such that A= CBUC)\ D.

A:

Q: On Z†, a * b = ab

A: if e is an identity element then it has to be satisfy a*e=e*a=a that is it has to be ae=ea=a which…

Q: Prove

A: To prove  tanxcosec2x-tanxsinxtanx+cosx=cos2xcosecx

Q: ja)Suppose that Fol= L{f(+)}, G(s) = L{g(4)} check it verifie -+(f(+) *g(+))}= F'cs) GcS) + Fs) G0)…

A:

Q: La) Emplain why is entive ? the function fcz) = 5z"-6+zcosz -ze

A: z=x+iy⇒5z4=5x+iy4=5(x4-6x2y2+y4)+5i(4x3y-4xy3) ---&gt;eqn(1)⇒xcosz=x cos(x+iy)=x(cosxcos hy-i sin x…