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Q: dx , if we let u =V 25 – x² , then udu = - xdx. (A True B False

A: Given query is to find statement is true or false.

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: 327. F(x, y, z) = zi+ xj+ yk; S is hemisphere z = (a² – x? – y?)/2. -

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Q: 3-Evaluate Fdr where 2X Cisgiven by rit) = t3+U-3t)rék

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Q: f (t) = 3e" cosh (In 2r -2t

A: Given,                 f(t)=3e-2tcoshln2t

Q: The DE : y' = e>x-7V is seperable Select one: O True O False

A: Try to separate the variables if it is possible than given DE is separable.

Q: dy 4xy+5y? can be transformed into a seperable DE The DE: xp xy +3x2 in x and z by using the…

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Q: 2.Evaluate . xy+ds where C is the right half of x2 + y? = 16

A: Integrate with use parametric form

Q: SI. 1dV, where B = {(x,Y, z): 1 < x² + y² + z² < 4, y 2 0}.

A:

Q: I shift as in Example 4.9 to find the general solu b. (2D – 1)²y = 0 + czx?)e2x

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Q: -R show that D-2D-31 =0 and hence find D", (b) Given that D %3D

A: inverse of matrix

Q: x=In i y=r2, find y " when For x=0• O 8 O 4 O 16 O 2

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Q: 1 Evaluate dz, where (i) C is z+ = 2 .2 +1 C

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Q: A P AB=AC 2m(DPC)=m(BPD)=m(BAC) Prove: BD=2DC

A: We will use triangle property to find solution to the problem .

Q: dt 20.5 t2+2t A - In|t? + 2t| + C B. 2ln +C C. In +C D. In + C

A: First we common out t2 from denominator and then put 1+2/t=u and differentiate both sides with…

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

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Q: The identity LiS L xyzdzdxdy = "/2 S Sa rsin@cose zdzdrd® x² +y² 1-y² x² +y² is

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Q: af Given f(x, y) = In(7x² + 9y²) then

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Q: EX: Verify that z= I+ V3i satis fies the 2. eq.

A: the given equation is z2-z+1=0 given the value of z is z=1+3i2 substitute the value of z in the…

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: Q111f и %3D (1 —2ху + у?)""/2, Prove that: ди ди y əx y? u3 У ду

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Q: r In y dr, where D is described by 1 < r < 2, e <y<e aD | V1 +r² dy, where D is described by -1<r<1,…

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Q: 198). Let c be (,0) to(4r, 0,0) G=) ydx+ xdx t Xyz dz Is 6CX Y,Z) independent of C?

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Q: There does not exist r E Q ə r² = 2 ylgn ihi

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Q: Find the general şolution_to the following. (D* - 2D – 7D? +8D+12)y = 0

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Q: 10. What is 2ri 2 fo, h (z) dz?

A: curve C3 encloses points of singularity z=-2 and z=0 in clockwise and counterclockwise directions.…

Q: * Evaluate SSS 12z dV E where E is enclosed z = x² + y? and z = 1 %3D Зл о 2л о 4л о IT O

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Q: -3y(In x)' +3x* (In x) y' =0

A: First simplyfy the given differential equation.Then taking integral on both sides and solve it.

Q: 6. SS dV に lies b/w ミ 25 %3D and x? f y? + z? Ź 36 in the firót oct ant ...

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Q: dz wher the integral fe z2 +9 C = 4 is

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Q: . If U = z sin y/x where x= 3r2 + 2s, y= 4r – 2s², z = 2r? – 3s², find a) Or b)

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Q: S- - ydx + xdy, C: y² = 3x from (3,3) to (0,0) 01 0 3 O 0 2

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Q: With the form of parhal frachun deomposition: A Bxt C A=1 (x-1)(x¥4) x-1 メー メ44 01 Evaluake x²+x+8…

A: The given integral is: I=∫x2+x+8(x-1)x2+9dx

Q: %3D otheowis Jiven that Pa) is apd f O find c ?!

A: 1) The value of c is obtained below: Given pdf is, f(x)=cx, 0≤x≤2 ∫02f(x)dx=1∫02cxdx=1   cx2202=1…

Q: 5Is there a value of r sotha X = 1 y = 2 and Z=r is asolution to the linear systen ? If there is ,…

A: Putting equations as;23-11-1241-2 xyz=11-712Augmented…

Q: What is r' (x) when r(x) = In ? Select the correct answer below: O Pu) = - Sr+1 O rw = - Sr+1 x) = !…

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Q: 10. f(x) =-x2 +3x+ m, y 4-IOBI = 10CI %3D A(ABC) = ? B.

A: As per guidelines, we will solve first question poste. 10) Given fx=-x2+3x+m 4OB=OC

Q: Evaluate SSS 2e(a²+y²+z?)"² dV over B where B= {(x,y, z) : x² + y² + z² < 1}. Take n = 3.

A: • The given region B has spherical symmetry, so it will be easy to solve this volume integral in…

Q: 7 2 dx dy y? 3 Evaluate the integral: Jo 98 3 294 3 196 392 3.

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Q: zlanstriduz.n 20 9. Hx) %3D 2. 7. a tom Where a and 6= %3D %3D

A: To find  the values of a and b.

Q: dz where a inside r= C z-a 2ni

A: We have to find integration of given function Using Cauchy's Integral Formula.

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

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Q: 11. f (x, y) = ery subject to a? + y? = 16 %3D

A: The objective is to find the lagrangian multipliers for fx,y=e2xy subject to gx,y=x2+y2-16. To solve…

Q: 5) *=ClSln t ,y =4 csst t=-2 %3D a) determine dy b) and graeh

A: we have to find derivative

Q: Vx Sn(l+x*) de 23/2

A: Using the substitution ... Explanation of the solution is given below...

Q: 37 Го fо7 (xsin(у) — усos(x) dxdy %3D 2 2

A: ∫02π/2∫03π/2(xsiny - ycosx)dxdy in this this is double integration so in first we take y as constant…

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

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Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.