Srwax - Sou) du. flw) sec (3*) 3x-1 Consider Solu) du ? %3D %3D what is O n Scos u du 1 3 In3 B In 3 Sco COs u du sin u du 3 In3 JSin Ssin u du In 3

Q: that Find flz)= r°cos20 + ir?sin po Such %3D is analytic-

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Q: I got 0 but idk if thats correct please show all work

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Q: D Question 2 Select all that apply: r y" + 3ry - 2y = In r 3rd order O linear Ononlinear O 2nd order…

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Q: 2ーてスース+スニ。 A ind yh ans: スi:z )スてニリ人3:)

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

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Q: If R = {(x, y) : 0 ≤ x ≤ 1,0 ≤ y ≤ 1}, then find (²+1) +2 0 1 arctan O 2√2 3 0 √2 3 O √2 3 (√³/₂2)…

A: Please see the below picture for detailed solution.

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

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Q: -tan(z) %3D z*+cos(z) dx Select one: O a. None 5sin(z) Ob. ²+coz² (z) Oc. O d. 0

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Q: If y(u) J5 COs v9 dv then cos(9u eIu y'(u) = %3D e4

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

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Q: What is the image of ALMJ by Ro90? Ro,90? a. AJKL b. AKLM c. ALMJ d. ДМJK

A: Here we have to find the image of the ∆LMJ by Ro,90

Q: Evaluate . 2y2 cos(x) dx + 4ysin(x)dy where C is the line from (0,0) to G,0) and then a line from (,…

A: Line integral over the curve.

Q: V, = {2i} m/s V, = {0.448v½i + 0.894v,j} m/s = {5 cos 0 i + 5 sin 0 j} m/s %3D 目。 Vb/r v, = 2 m/s 5…

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Q: 4) For A = ajax + azāy + azaz , B = b,ax + b2ay + bzaz, show that A.B cos 0 = A.AVB.B

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Q: dy If tan(ry) + 5 = ry then show that dr? 2y

A: Differentiation two times

Q: On taking AABC, use cosines law: 450 300 500 Om)* =(450 m)* +(500 m)* – 2×(450 m)(500 m ) cos A…

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Q: Find the area lying outside r = 4 cos 0 and inside r = 2+2 cos 0.

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Q: Evaluate: / sech[in cosr Janx dx A -2 tan-1(e cosx) +c cOsx B) None 2 tan -(e cOx) + C COSA D - 2…

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Q: 1) Let c. 12i| =3 and I = e dz. then %3D I= 1o TTi? %3D

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Q: Consider the following figure. D F OC = 8 and OE = 4 OE I CD in 00 Given: %3D Find: CD CD =

A: Answer

Q: 2) al X,X2 =) y = Xi~ ? ,-,Xn ~lid exporen tíal ( 100 b) Xq, X2,--- Xn~ iid N(44i44)= ビ- ~? i=1 %3D…

A: Solution : a) Given : xi  ~ exp ( 44100 )   ; i = 1,2,3,...,n ∴ θ = 0.44     Y    = ∑1n Xi It is…

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

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

Q: I don't understand how they got 10 square root of 6?

A: Given,

Q: Let C, be the rectangle with vertices (0,0). (1,0) (0,2) and (1,2) oriented counterclockwise. Find J…

A: Green's theorem problem....

Q: 1/w cos Tº If h(w) = 10 -dz then h'(w) = (m),4

A: Given:-h(w)=∫101wcosx9x2dxTo find: h'(w)

Q: N is the centroid of triangle HIJ. If KN=9, IM=15 and LN=5. Find KJ K. N/

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Q: %3D 20 24 tan 24 through solve this egni: Hint :oU=KL +2 =0 மு 3K²=Par ET %3D 2.

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Q: Compute the length of the cardioid r = 9 – 9 cos(0).

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Q: 21. xª sen z dz -z' cos z + 3z² sen z + 6z cos z 6 sen z + C %3D

A: see below the answer

Q: -41 sin tZ dz, c: 1Z-il=2 z4 ans: 3. coshz dz ,C: IZ1=1 27T ans :

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Q: ,32 Let C: z-il=3 and I = -dz. Then %3D z2 1=0 None of these O I= 4nti O I= 6ni O I= 8ni

A: The solution is given as

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

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Q: 12(иxx + uy) %3D3ии. 0 <х< 9, 0 <у<3 и, (0, у, t) %3D 0, и, (х, 0, е) %3D 0, и (х, у, 0) %3D…

A: We are given the following system.       12uxx+uyy=3utt, 0&lt;x&lt;9, 0&lt;y&lt;3…

Q: dz az If z = xyeX/Y, x = r cos(0), and y = r sin(0), find and ar when r = 2 and 0 = %3D az ar (r, 0)…

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Q: a?u, a?u (c) = 0;0< x5 5,0 sys 10 əx² ду? subiect to

A: Given,     ∂2u∂x2+∂2u∂x2=0;      0≤x≤5,   0≤y≤10    ...(1)subject to      u(0, y)=u(5, y)=0; 0≤y≤10…

Q: Find the length of the cardioid r = 1 – cos 0.

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Q: Express Q(x) = cos4 (x )+ 12 as the composition of three func-tions; that is, identify f, g, and h…

A: Q(x) = cos4 (x )+ 12 We need to express the given function as a composition of three functions  that…

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

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Q: Find C if r(t) = ⟨et, 3 cos t, t + 10⟩ + C and r(0) = ⟨0, 0, 0⟩.

A: We have given function r(t)   r(t) = ⟨et, 3 cos t, t+10⟩ +C   We have to find the value of C   It…

Q: ,3 Let w = x'y cos(2z). Find the following. dw (a) (x, y, z) = (b) (x, y, z) = ду (c) (x, y, z) = dz

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Q: Question 2: Show that the set S = {rVT + V2:rE Q) is dense in IR. Explain and show your work.

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Q: Find the values of z satisfying cos Az = 0 2

A: Result : General Solution of  cosx=0 is x=(2n+1)π2

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

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Q: dy _ 2y 4. If tan(ry) + 5= ry then show that dr?

A: We have to do differentiate with respect to x.

Q: ди Ans, u = e"(A,er" cosh ax + Bjehar" sinh ax) e ka't cos ax + B,e¯ha" sin ax) -ka’t, u = e"(A;x +…

A: Given PDE is k∂2u∂x2-u=∂u∂t,  k&gt;0          (1) Let the solution be u=XT, where X and T are the…

Q: 11 z- CCW -dz, z2 - z de. c:|2- = sec(u), <ý<.cv Question 11) Find I =

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Q: A) Let w = 4x2 +4y² + z?, x = p sin o cos e, y = p sin o sin 0, z = pcos o. Find aw/ap, aw/a6, and…

A: "Since you asked multiple questions we will solve the first question for you. To get any specific…

Q: 22-j is 1. -1+jZ If Z = cos 0 + j(1+ sin 0), show that the magnitude of

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Q: Consider the model Yi = β0 + β1Xi + εi, where E(εi) = 0 and Cov(Xi, εi) = 0. We observe (Yi, Xi)…

A: Given Model is y=β0+β1Xi+εi where, β0= Intercept Parameter β1=Slope parameter εi= random error…

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.