K (To - T) if 0

Q: The ODE ty" – 3ty' + 3y = t* has a particular solution Yp(t)

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Q: if x~unif. (0,2),find the U.b. of p(lx - mul>= 2)

A: Given X~Unif(0,2) Result: if X~unif(a,b) then  Mean=(a+b)/2 Variance=(b-a)2/12

Q: 7) if p(X) =- ) , and grea) =0; g'LW)=), Find f'la). %3D

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Q: 2. given that y = 0 at r=1

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Q: Find the x -value of the point on the curve y=V/2x+2 that is closest to the point (8,0). x=6 O x= O…

A: To Determine: find the x-value of the point on the curve that is closed to the point (8,0) Given: we…

Q: 1.2.10 1 if x < a, f (x) = 2a elsewhere on (-T,"|, where 0 < a < T. Sketch for two different choices…

A: Since, you have post multiple question here. I am answering first one. Please post again with…

Q: The ODE ty" – 3ty' + 3y = t³ has a particular solution Yp(t) t3 + 5In t| t3 8. +In |t| 4 O t3 5 -…

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Q: If e dy then y-

A: We will evaluate the following Integral.

Q: If u = f(x), then ſ dx x++2x²+1 k + C for some constant k . Compute kf(1). x2+1

A: We have to find kf(1) Given that: u=f(x),∫xx4+2x2+1dx=kx2+1+C  for some constant k

Q: ду h. ax if cosh(3x²y) = x + In(e*y + 1) i. If fx se and fxx arz find fyyxxx if f = x³y² – – Y əx…

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Q: Find g'(3). g(x) = In(1+t) dt In(4) 6ln(10) O In(10) 3

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Q: 4x obtain the section of the equation Ex xl with the condition u oon X4

A: Let us consider the given PDE is P(x,y,u)ux+Q(x,y,u)uy=R(x,y,u) The equation is solved as Determine…

Q: 14. Find X(s), given x" + 16x = t, x(0) = 0, x'(0) = 0.

A: answer is in next step

Q: Find the linearization of y = eV1x at x = 36. (Use symbolic notation and fractions where needed.)…

A: We have to find linearisation

Q: 1. Find the following. Iy(-1, –1) if g(x, y) = x³ – xy² + 3

A: Given g(x,y)=x3-xy2+3 Differentiating g partially with respect to y, gyx,y=∂g∂y=0-x(2y)+0…

Q: If E(X") = (r + 1)! 2", then, the moment generating function Mx(t ) = E(eXt) is (1-2t)2 False True O

A: If we Calculate first moment by using both the expression. It should be same otherwise it is false.

Q: For z > 0, 옮(1 In (t³ + 1) dt A) In (x³ + 1) B) In (8z³ + 1) c) 2 In (z³ + 1) 2 In (z² + 1) D) 2 In…

A: Solution: Consider the given that; ddx∫02xlnt3+1dt We have Leibnitz Rule: ddx∫a(x)b(x)f(x,t)dt =…

Q: Let SINGLEDFA = { | M is a DFA and for all s e L(M),|s| = 1}. Show that SINGLEDFA is decidable.

A: Detailed explanation mentioned below.

Q: Find the length of the curve y = In(e - 1) – In(e + 1), In 2 sxsIn 3.

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Q: 3.4.2 Assume that Y, the number of minutes it takes you to eat lunch on an average day, is equally…

A: We can assume that Y~ Uni(a, b) where a=30 and b=40   We know that f(y)=1b-a        for a&lt;x&lt;b

Q: 2) Suppose that d₁= .02t 0≤t≤2 0034² 2<t≤5 Suppose that a deposit of X is made at f= 0, and a…

A: We have to find required deposit amount.

Q: 3. If f(x, y, z)= In xyz te(3.0²), find f,,f, and f-· 4

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Q: If z + In(e3* - e + e²) = 0 dz find at the point (0, 0) -3 -2 3. 2.

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Q: FIMD dY IF x= AMD Y= U 1tu3

A: Let's find.

Q: 1 0 Problem 4. Let p(x) = 5x? – 3x +2 and suppose that A = 0. for some y E R. Evaluate p(A).

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Q: kx 4+x² If k > 1, evaluate O ka -In|x² + 4 +C 2 Okx -arctan (2x) + C 2 Ok In(x² + 4) + C O arctan…

A: Given: I=∫kx4+x2dx   ...1   As we know the common integral. ∫1ax+bdx=1alnax+b+C

Q: Suppose that F(s) = ℒ{f(t)} exists for s &gt; a ≥ 0. Show that if k is a positive constant, then…

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Q: 2. and XR %3D C. Two tails with n = 34 , x =

A: Solution: From the given information, level of significance is 0.01 and n=34.

Q: If Σ An diverges then > can diverges O only if c>0 O only if c< 0 O only if c+0 O for any real value…

A: Given, the series ∑an diverges, then we have to find the values of c for which the series ∑can…

Q: s at x =-1 and x = 2

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Q: 10.Show that Φ(t) = Ψ(t)Ψ−1(t0), where Φ(t) and Ψ(t) are as defined in this section.

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Q: Find y' for each of the following. e2a+3y = x2 - In (ay³) %3D i.

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Q: e. y= (x² + 4)/x in the interval 1<x<4. 8+ 4ln4 - % s.u ans.

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Q: Ln 寸 M C MacBook Air 21 22 of'(-1) ~ -3 of'(-1) × 3 o f'(-1) ~ –10 4. 3. 2- Sp8乙k +++ 2+ 2. 3+ 4. 5.…

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Q: Suppose f(x) is positive, continuous, and f'(x) < 0 for all æ in [ – 8, 4], and| f(x)dx = 76 and L…

A: Concept: Mean value theorem: The mean value theorem states that if a function f is continuous over…

Q: a'(t) = -x(t – 1), x(t) = 1 on [-1,0], is given by 1(t) = E(-1)* t – (k – 1))* k! for n-1<t <n, k=0

A: As per the question we are given the following first order time varient differential equation :…

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: d If g(x)=- S* [e²-In (21+1) ]dt, find g(x). -2 2 (2x + 1)2 4 B (2x + 1)² Ⓒe-In(2x+1) 4 (2x + 1)² di…

A: A function is given by, gx=ddx∫-2xet-ln2t+1dt. The objective is to find the second derivative g''x…

Q: The ODE ty" – 2ty' + 2y = t has a particular solution Yp(t)

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Q: Find fCx) if flo)=0 and the tanGat (k,F CX) has ine af Slore x(x+2) a

A: Given for the function F(x), F(0)=0 and tangent line to F(x) at x,F(x) has slope xx2+23.

Q: e 2t In (1+7) t lim t→+o t1/2

A: Let L is the value of given Integral.

Q: If z3 + In(e 2 -2 e+e) = 0 az find at the point (0,0) O -3 0 3 О-2 O 2

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Q: If we know that E (") (x" 1) = ("†").t then show that Eo (") -C") r3D0

A: Given information: The given theorem is:

Q: 3) Find the general solution by using reduction of order method to ty" – (t + 1)y' + y = 0 given…

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Q: Suppose f( – 1) = – 8 and f'( – 1) = 7. Find the following. E (7z² – 10z – 6) S(z) at z = - 1 is…

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Q: ds if s = dt t Find 7t +2

A: S=t7t+2 We need to find dSdt

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.