A) L{t//4} : (5/4)! a+5 B) L{u-2(t)} C) L{e"u(t)} 8- 5 3! D) L{t*e"} = E) e{icm (;)} 5Cos s(s – 2) 82 + 2

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: Evaluate S, 5y²dV where E is the reqion below x + 3y + 6z = 9 in the first octant.

A: we need to evaluate the integration over the region using the triple integral. First we will find…

Q: 1. Aşağıda verilen serilerin yakınsaklık ya da ıraksaklığını belirleyiniz (Yöntemleri açıklayınız).…

A:

Q: dn-1 for all n E Z with n > 2. Prove that for a 2. Let d = 2, and d, neN, d, =. %3D %3D %3D

A: Mathematical Induction is a special way of proving things. It has only 3 steps: Step 1: Show it is…

Q: 35 - A 3x7 matris ve rankA = 3 ise nullity A = ? O A) 4 O B) 3 OC) 1 O D) 0 O E) 2

A: Answer (35) Given ,  A 3×7 matrix where rankA = 3  We have to find nullity A

Q: .'( , "ג oa3 (125x*y)" 学 A: 125 2 3 $%% 1/3 5メ Y C: D: VONE OF THESE

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: 6. Prove that for x > -1 then Vn E N, (1 + x)" >1+ nx .

A:

Q: 7 y=tanx show thats y" = -2Siny cosy 1f y=e Snbx show that:

A: Dear Student, according to the Bartleby guidelines, we can answer only first question if multiple…

Q: /9 – 2° dz Integrate: z4

A:

Q: 13. the , xydA, where ySxsy?}

A: First I have set the limiting double integral from given information and then solved it .Final…

Q: Show Sn+3 diverges by osing 6n +5 the test for divegence 1こV

A:

Q: 2. If z = x° In 2.xy, find at 1,-

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Q: 7) Use Theorem 7.1.1 (Table) to find L{f(1}} for the following: S)-(e*-e*)}° a.

A: The given function is f(t)=(e-3t-e5t)2. Expand the function implies, f(t)=e-6t+e10t-2e2t The Laplace…

Q: 2² + e4 z lim z 0 22 – e²

A: This is a form of infinity by infinity so we have to apply Lhospital rule that is differentiate both…

Q: -8 6. Evaluate the integral +y² dydx

A:

Q: 1 prove that | e -ym dy = mr(m) -ут

A:

Q: ー28- Sa Oclumina f dz sabishy cauchy- Reimon quakir f andlgove @ frz= J-2xy ti C-Xyz] +z* @ f(2)=…

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Q: 4. If x = cose + isin0 & 1 + V1– a² = na then prove that 1+ acose =(1+ nx)(1+) %3D 2n

A: Given, x= cos θ+i sinθ and na=1+1-a2      To prove:  1+a cosθ=a2n(1+nx)(1+nx)       Let  x=…

Q: S Prove that L(cos 3t) : %3D (s2+9)

A: We know that Lf(t) = ∫0∞e-stf(t) dt Then Lcos 3t = ∫0∞e-st cos 3t dt                             (1)…

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

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Q: Example 8.10. Evaluate Sº (ii) Simpson's 1/3 rule, (iii) Simpson's 3/8 rule, dx Jo. 1 + x² by using…

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Q: Prove by mathematical induetion. Ine I+2 +2+2 +2° = 2.

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Q: 8-1 5 + 5s4 + s³ s² + 4s +3 table or not using Bor using Routh cri

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Q: az Find for z = x'y'eV

A:

Q: Q5) Evaluate the integral 0.61-10 (6.73x + 4.3025 - 10- dx 2.316 • 10-11 122-10- Using trapezoidal…

A: The solution to the integral can be calculated using numerical methods. The formula for the…

Q: Evaluate S, 5y²dV where E is the reqion below x + 3y + 6z = 9 in E the first octant.

A:

Q: Obtain the general soluti d²y 1. 7- y = 10sin²x

A: Given: d2ydx2-y=10 sin2(x)

Q: 6. Consider the ODE system below f = y? - ,2 = y +?. Which of the following is true? a. Solvable by…

A: Here we have given two differential equations. For a system of ODEs, we can use the elimination…

Q: 2. Z=e Iny

A: Given that, z = ex ln y x = ln (u cos v) y = u sin v We have to fin dz/du and dz/dv. Then we get,…

Q: (b) f(z) = tan¯"(5z) - (In(2"))®

A: We have to find derivative

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

A: Solution

Q: dy then In z is If y = cosh z

A: Without wasting any time, any further, differentiate the RHS to get your answer.

Q: If utt 4ura u(x, 0) = e", u4(x, 0) = 0, u, Ux → 0 as x → ∞, then u e* cosh(2t) O e2 cosh(4t) O e2¤…

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Q: 11 ComputePydz - zy'dy, nhere Dis descnbed by z² + y²s1. -1/2

A: Given an integral : ∫∂D x2y dx - xy2 dy  where D is : x2+y2≤1 We need to compute the integral.

Q: (x) = 3x +12x+2, %3D ues of a, b and c such that

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Q: 13- dy + 2xy = y diferansiyel denkleminin genel çözümü aşağıdakilerden hangisidir? -x* +c1 y = e a)…

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Q: 4. Exercise §3.4 #47. Let n €Z with n> 0. Prove that E - a(n)

A:

Q: 6. Find the fized point of flx) [-,1] where', on fa = (동) x-(올)x3

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Q: 8. Theorem h° = %3D

A: The figure given below represents the circle. From the angle subtended by the same arc theorem, The…

Q: 7) [[3embch5y] dvl [jel*5) dy] „In[sec h 5y]

A: Using rule of logarithm & integration formula of sech(x)

Q: 6. Consider the following model: Yi = Bo+B,D11 + B2D21 +u; O if person i is a non-immigrant) where…

A: Dummy Variable Trap: It is defined as the scenario when the attributes are highly correlted. One…

Q: If f(x,y,z)=z In(x²ycosz), then fz is O 2z X OZ y O2z y O In(x²ycosz) - ztanz <|N

A: This question is related to partial differentiation, We will solve it using given information.

Q: D Reduce the Q.F 22,xz t 22,X3 2ズュズ3 weag ayf of oothogonal toans fermation by an Ans: y+92-295

A:

Q: 5) why is x3- 3x +I X +2 Conti nuous (0,00) on where is it discontinuous?

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

A: Given      f(x) = 1512-3x

Q: 13. Use the chain rule, in Leibniz notation, to find dx dy at the given value of x. а. у %3D Зи? —…

A: We are solving the first three subparts and for the next subparts post the question againand also…

Q: 16.1. Use an antiderivative to show that for every extending from a point 21 to a point 22 2" dz =…

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Q: 2. In AXYZ, PQ || XY . If XZ = 15, YZ = 12, and ZQ = 8, what is ZP? 2.

A: Use concept of similarity. In similar triangle, ratio of corresponding side are equal.

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.