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Q: ду Let y = In Vx² + 2z3 + cos(b³), find

A:

Q: Verify that cos kx is a rolulion Also, stafe what kind of DE is the DE above :

A: This question is about solving differential equations.

Q: If z = cos (x + ay) + sin (x - ay), with a ∈ R, then the result of a(∂z/∂x) + (∂z/∂y) corresponds…

A: If z = cos (x + ay) + sin (x - ay), with a ∈ R, then the result of a(∂z/∂x) + (∂z/∂y) corresponds…

Q: If u = x² cosy+ ye", where x = s+2t and y = st, prove that ди ди 2- (s – 21) (x siny- xye – e"). -…

A:

Q: Compute the Jacobian of : O(r, 0) = (9r cos 0, 4r sin 0)

A:

Q: Let r(t) = (t, 3 cos(t), 3sin(t))

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Q: 2 write Dirac Delta beinction and it's laplace trans forms.

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Q: 4) For A= a,āx + azay + a3az, B = b,ax + bzay + b3az, show that %3D %3D A.B cos 0 = A.AVB.B

A:

Q: Z2 in H = {0,4,8} find all left cosettes

A:

Q: Since Cov (X, Y) = E [X, Y] -E [X] E [Y]. Obtain Cov (Yi, BO)

A: From the given information, Consider, the regression equation be assumed as given below:…

Q: -W : By the same way, prove that g Z sinWo sinw.k Z -27 cus Wo +1

A:

Q: 2. Let f(r, y,z) = In(r² + 2) + ye* – cos(2yz). Find faya- COS

A: see below the answer as per bartleby guideline we have to solve the first question onl

Q: and casy=0t, and DLyr, Furd the exact alue of tan Ca-y.

A:

Q: Ở. verify that y10) is a constont soluion b. Find all Solurions to DE C. Find two dirrerent…

A: According to the problem, we have

Q: Form a DE with respect to t: x = Acos (In t) + Bsin(In t).

A: Sol

Q: In r dy If y , then is cosh z

A: Straightway proceed to differentiate both sides,

Q: 0/ the Valke of & that makes the Velteof the fumetion 2.

A:

Q: التاريخ اليوم موضوع الدرس A) Discuss the conrergence of facx) %3D on A = Co,0)

A: Convergence of the sequence

Q: evaluate the triple iterated integral.

A: Given: ∫0π4∫0π4∫0cos∅cosθ dρ dϕ dθ

Q: Express the following to rectangular form. 1. z = v17(cos346° + isin346°)

A: Rectangular form of complex number is defined as z=x+iy Now simplify the given complex number to…

Q: H.W: if w x2 + y2 + z2, x= e*Cos6, y-erSin0, z=e0 prove that aw/ar= er/w and aw/a0 = e20/w

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

Q: Suppose that Wi is a standard Brownian motion and consider times 0 < s <t<o∞. Find E[W,W¿] and hence…

A: Given: Wt is a standard Brownian motion  0&lt;s&lt;t&lt;infinity

Q: (a) /3yin In (g) dy

A: First remove the constant and then substitute the formula by integrating by parts and then simplify.

Q: Let w = x*y cos s(4z). Find the following.

A:

Q: T/2 COS z xp V4 - sin? a

A: givenI=∫0π2cosx4-sin2xdxsubstitute  sinx=t therefore limits will change t=sinπ2=1  to t=sin0=0after…

Q: Classify the Stries as nbsolurehy linvergen ti Condibinally lonvergent, divergent 18 K Sin

A: First we  recall some definition-1)  p-test for convergence of series ∑k=1∞1(ak±b)p :     A series…

Q: write a in the form a = aTT + aNN at t = 0without finding T and N. r(t) = (2 + 3t + 3t2)i + (4t +…

A: we have to write a in the form : a=aTT + aNN  at t=0 without finding T and N where r(t)=2+3t+3t2i…

Q: which u-sub will help integrate this? A. u = dx 11 [arctan(x)]" dæ = [9 + 12 cos(x)]" B. u 9+ 9x2 C.…

A:

Q: Express the following tunctrons in the form u+iv f(2)=In (I+z)

A: Solve the given problem.

Q: (b) If u =x cosy+ ye», where x=s+2 and y= st, prove that 2- ds du - (s - 21) (* siny-xye -e").

A:

Q: In the case when U = x on the edge y = a (where Yo is a constant), a calculate C, inorder to show…

A: Given at y=a, U=ψ0ax     …Equation(1). And, on substitution of y=a in expression…

Q: 1 By writing u y", and using the chain rule, show that 0") = nyn-1. dx

A:

Q: Use Green's Theorem to evaluate >[2²y² dz + (yz²³ + y²) dy where Cis shown below. 90 O-384 O-48…

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Q: If u =x² cos y +ye», where x =s+2t and y= st, prove that ди 2- Əs ди 3 (s— 21) (х' siny — хуе" —…

A:

Q: 7 the n ya In Cx? _y?) Do not Equatio InCx-yリ Do not check modificd Laplace

A: This is a problem of partial and Laplace.

Q: Calculate $ |z|=1 z²e¹/z cos(1/z) dz.

A:

Q: L[t cos 2t

A: Please find the detailed solution in below images

Q: Show that J, (z cos0)d0 = - R/2 os e)de = 1-cos z %3D 21

A:

Q: Let fln) = e cosx, sx %3D Express your answers in exact form.

A:

Q: Let w = x*y cos(42). Find the following. (a) (x, y, z) = %3D (b) (x, y, z) = ду (c) (x, y, z) = dz

A:

Q: If z = exy where x = In(u + v) and y = sin(u-v), find az and az du

A: We use the partial derivatives and chain rule of differentiation to answer the given question.

Q: Verify that cos kx a solulion of Also, stafe what kind of DE is the DE above

A:

Q: a. Show that W[5, sin2 t, cos(2t)] = 0 for all t by directly evaluating the Wrosnkian.

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Q: Let f(r, y, z) = In(x² + 2) + y?e - cos(2y2). Find feyr-.

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Q: if z, = (1 – v31) and zz = (V3 + i) by De Movier's theorem z,z– 4% = 1 (cos( +5 + isin +5)

A:

Q: Co

A: Given that: The Taylor series for f(x) = ln (x) at c = 3 is ∑k =0∞ ck ( x - 3)k .

Ratios

A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.

Trigonometric Ratios

Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.