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Q: f= x? + क) | + ला (i) of =? (üi, af मु] liv) of

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Q: oS% (x? + y? + z*) dz dy dy

A: Solve the following

Q: Evalnate the SSce'tzxy+j) dydx when SterSizeof x =0:2 and s óep sizcof y-o.8

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Q: Evaluate ff, x² In(y + 1) dA where R = [0,1] x [0,1].

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Q: Find r'(t).

A: We have to find r't: rt=4ti+t2tj+lnt2k We know that dxndx=nxn-1d lnxdx=1xd lnfxdx=1fxd fxdxdxdx=12x…

Q: Evaluate : J x dx, where neN.

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Q: %3D 니e?. H(t-1) + et.8t-4)

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Q: Given y = , y (0) = 1, h = 0.5. Find y (2) using the fourth-order RK

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Q: dx If - = Sh(8) d®, then h(0) de = ... V(4+x2)3

A: We will make use of only the basic techniques of integral calculus to solve this question.

Q: %3D 7. If mBC = (9x – 53)' and mCD = (2r + 45)", find mBAD. E

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Q: 7 .TT/2 *3 [¹²³r r cose dr de dz

A: Given: I=∫-17∫0π2∫03rcosθdrdθdz   We know that; The Power Rule: ∫xndx=xn+1n+1+C The common integral:…

Q: ex (플 +c) %3D

A: We are asked to graph the function.

Q: d? -(A+B) at t = 1. di?

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Q: J) 11"+2 + 122n+1 divided by 133 , Vn E N*

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Q: what is the DE for this?

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Q: T scosce) 25-r2' 2. dz dr de 0 0

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Q: Evaluate o y dæ – x*dy,

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Q: R=(aL/bL+1)-c Slove for L.

A: The given formula is, R=aLbL+1-c.

Q: dz where c is |z=1 z'e? Evaluate

A: ∮ f(z) dz = 0 when no any singularity lies within region of integration. But if any singularity lies…

Q: 3. Find x in ДPOR. R 12 О 13 О 15 О 16 O v60

A: We have to find value of x

Q: 2) What is the relationship between 2J andOZK? K Supplementary Adjacent Vertical Complementary…

A: If sum of two angles is 90 degree. Then the angles are called complementary.

Q: Cosot tunpt H %3D then G)= 22

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Q: sec? (1/x) dx. 9: (16pts) Evaluate

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Q: dw -is equal to: dv If w = 5u, then 5w5 v(1 – 20u In v) 5w v(1 – 20w5 In v)

A: Given, w= v5w⁴ To find, dw/dv

Q: ex iR Py, z)-0 fined diz H and x=2-4

A: We have to find partial derivative.

Q: =dx V7x +c O None 10 VA +c 10A +c

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Q: ds Find dt S=- 3tan t-et

A: Given, s = -3tant -e-t   We have to find the value of dsdt

Q: Given the following, calculate Var (T20). i. eo = 25 ii. l, = w – æ, for 0 < x <w.

A: Given information: Given that e0 = 25 and Tx is the future lifetime random variable.

Q: Find in side r=2 aren oul sde r=l+ Ges 6

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Q: SP: PR = 3: 2 %3D 160 R S.

A: We are given the following figure. We are given that                   .

Q: ind a suitable A and B so that: A< S, Vx + 4 dx < B

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Q: During a polytropic process, the ideal gas changes state from 20 psia and 40 F to 116 psia and 338…

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Q: Consider --e +y?). 3+3² Evaluate dxdy

A: We have to find partial derivatives for the given function.

Q: + y + z = 1 in the first octant.

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Q: Evaluate 2z dV, where E is the solid hemisphere r +y + 22 0. E

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Q: If z = x² dz = Az = - ·xy + 4y² and (x, y) changes from (1, −1) to (0.96, −0.95), compare the values…

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Q: nd ,I:J ar

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Q: Evaluate Conditions. pum テ=(6)V:s「(4s te return

A: In 2 quadrant sinx and cosecx is positive. Otherwise, all other trigonometric values are negative.

Q: Write a in the form e(=) and hence find - [x*] for x > 0. dz

A: The given function is: xx=eln xx    =ex ln x

Q: y"+ay'+sy= ーア e'sent y ro)=0, yto) = 1

A: Given differential equation is y''+2y'+5y=e-TsinT y(0)=0 and y'(0)=1 yT↔Ysy'T↔sYs-y(0)=sY(s)

Q: dx Evaluate xV x2 - 4 TT 2 4 O O

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Q: Identify the secant: H/ BA C F O Line DF O Line HG O Line AH Line BH 7.

A: A secant is a line that intersects a curve at atleast two points. For a circle; if a line cuts the…

Q: 7w ° sec(w *) tan(w 4) dw ec(w*) n(w¯ª) dw

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Q: af af and dy Find

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Q: wx + yz = bc, for z II

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Q: rer, Evalua den (3x1 fnd C: lve Segeant Co0) to (4,2)

A: Line Segment:    Each portion of the line segment can be labelled for length, so you can add them up…

Q: Evaluate SSS9e=+y²+=?)** dV over B where B = {(x, y, 2) : a? + y? + z? < 1}. Take = 3.

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Q: Evaluate 22 dV, where E is the solid hemisphere x +y² + z2 0- E

A: The given region E is x2+y2+z2≤4 and z≥0.Considerx2+y2+z2=4z=4-x2-y2Put z=0,thenx2+y2=4It is circle…

Q: у — За)dx + (: urve passing thro tisfying the diffe

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Q: a) b) Compute E(X|y), Var(X) and Var(Y). Hence, deduce the value of p= Corr(X,Y).

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