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Q: 10. dr S f(æ) dx = Choose...

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Q: 2|x~ Bin (wa) X~ TI (Q) = -IN 0 QE [011] you should Find posteria 8201 other wise

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Q: (7) In general, (SOT)CSnT.But, (SnT) + SnŤ.

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Q: 4. 5 Show that if y%= x+4 then dx (x+4)** %3D %3D 16. dx. 2 (x+4)² **n Hence, find the value of|

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Q: 2 Exercise.8 Find: P4 (x), Pg(x), L P¾(x) P3(x) dx , LIP,(x)|² dx

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Q: 3- S e J coscinx) d

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Q: 1-y² L In (r* + y? +

A: Introduction: The process of determining the area of the region under the curve is known as…

Q: 2. 17ァーーレス+ら)dx Sim pricy the anw ser =

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Q: 2 If In(ax)dx = 3, then a = %3D %3D 1 4 4 e4 4 ез 4 O None

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Q: If h(x) — За — — 1, j(x) k(x) = 21x? – 26x – 11 , show - 7x + 11 , and - - - - h(x) · j(x) = k(x).

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Q: Is it possible to find a number  n  such that is ∫0∞  xn dxconvergent?

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Q: 13. Find ML. J 3x + 11 K N 45 7, 10x - 12

A: According to guide and we should have been able to do only one question at a time #13

Q: x*y" + xy'+4y= 2x Ina

A: Cauchy linear differential equation

Q: if M Z- Sin (xy) fined 4 22 y= lint t-1

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 36 – y8 -dy y5 Integrate:

A: SOLUTION-

Q: Evaluate the integrals

A: 37. ∫112142dtt+4tt38. ∫0edyy1+(ln y)2

Q: 2. Estimate the value of V22. + • V22 is between and but closer to Decimal estimate: 22-

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Q: | Va(In(x))° dr (ax) 1.

A: We find the integration by substitution.

Q: - S e-ttat1-1 dt a # 1 a '0

A: We use the definition of the Gamma Function to solve the given question.

Q: 1. Differentiate the following with respect to x: a. y= 5x - + 5Vx + 3p ex + In(x) - 7 (9)

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Q: (b) f(z) = tan¯"(5z) - (In(2"))®

A: We have to find derivative

Q: ronskian of the DE : xp(x)y' + 3y = 0 = er² et? et?

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Q: he coefficient ao of Fou +2 t. く?

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Q: (14) Approximate S, x² ex², Using Simpson's rule dp,

A: Simpson's rule is a numerical method used to approximate the definite integral which represents the…

Q: 129. y = ecos i dt In

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Q: it is unbaised estimated of a Then Show That ta is baised estimated of O2.

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Q: Is there a way to solve this w/o using L'Hospital's rule?

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Q: M N * LN = MO SS SAS AAS AONL E AONM ALON E AMON ALNO S AMON

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Q: az given that yz*+x2z3 = eyz ax

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Q: 2 If [ In(ax)dx = 2, then a %3D 1 e4 4 None es 4 4 4

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Q: B/let Flx)=[X]-X,x E(-2,2).which valuesof x o E(X) continuaus?

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Q: find the derivative.

A: On simplification, we get

Q: c). Invest diFrgate whether the given en equation is homogene eous dy 2. oxy

A: A first order differential equation is homogeneous when it can be written as a function of y/x, that…

Q: 6. Evaluate 1 x² + y² + x² dV, where E = { (®,g, z) |1< n? +g? +z? <4}.

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Q: It is known that mortality follows De Moivre's law. If Var (T(50)) = 192 , calculate w Instruction:…

A: According to De Moivre's law, if sx=1-xw then Tx follows uniform distribution in the interval 0,w-x.…

Q: 4 In GL(2,Z13), det 1 4

A: We have to find the determinant using GL(2,Z13) That is, instead of usual addition and…

Q: (7 In GL(2,Z,), det O 35

A: Option 1 is correct.

Q: + 4 (A In(x² + 4) + C B arctan() + C (C) jarctan(;) + C -arctan() D arctan () + C

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Q: 5 Evaluate ſ“ S" r² sin ø drdøde 0,

A: Evaluate: ∫02π∫0π∫05r2sinϕdrdϕdθ

Q: 4 In(t) dt

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Q: 10- If f(u, v, w) is differentiable and u = x - y, v = y - z, and w = z - x, show that fe fe fe = 0.…

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Q: 1. Let x (x,) E l. Find x if 11-- a. x = 2 %3D

A: This is a question of functional analysis in lp space.

Q: Show that S ťe dt = 3VI

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A: Given that the tangent line touches the curve y = f(x) at (4, 3) passes through the point (0, 2).…

Q: 2 If [ In(ax)dx = 3, then a = %3D es 4 e4 4 O None e3 4 e6 4

A: Given that: ∫12lnaxdx=3

Q: Suppose / (s) - (÷)*" valuate: Js(x) dr +C 3- In (5)

A: Given      f(x) = 1512-3x

Q: 13. a) Show that EX=o (-1)*(")=0, and then verify that ) +C) + C) + - - G) +G) + () +- ... = b)…

A: We will use of binomial theorem to solve it

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.