Prove 0 + 1 + 2 + 3 + ...+ n = (n(n + 1))/2

Q: s function h(x), we have

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Q: (i+sinx cosx) sinhy dy 6- Cos 2X

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Q: 1 L(5x)sin dx dx+ J, (5x – 15)sin| 1.5 1.5 1.5

A: We will use integration by parts here  ∫u.v dx=u∫v dx -∫dudx∫v dxdx

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Q: Performs the following operations on the indicated system a) 777.75; + 67.57; =

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A: The differential equatio.n for a LCR circuit is given by…

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Q: a) 4°N®° =(ANB)° b) 4°UB°<(AUB)° c) if A°is open then the largest open subset of A is A°. d) All the…

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Q: log,(2x-1)= 2. Find x

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Q: A population of middle school students contains 160 sixth graders, 180 seventh graders, and 140…

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Q: J, (5x)cos( 1.5 15 Jk + (5x – 15)cos(- dx 1.5

A: We will solve the above integration as two parts. let f(x) = (5x) cos (nπx1.5)     and     g(x) =…

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Q: Express all answers in Rectangular Form. 1. (1 + j3)z² + (5 + j6)z + 7 – j6 = 0 2. 3z? – (5 – j4) z…

A: Since you post more than three subparts questions as per our guideline we can solve only first three…

Q: 3. A student council consists of 8 students, with 3 women and 5 men. a. In how many ways can a…

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Q: Σ S(0.881)" n=1 8.

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Q: You want to purchase a house in 10 years. You estimate the cost will be $184,500.00. You want to…

A: Cost of house = $184,500.00 Down payment = 20% = 20% of 184500.00 = 20×(1/100)×184500.00 =…

Q: %3D MUTM az əz +y= əz X- dv ay TTM UTN

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Q: (b) Find the solution of the following initial value problem y" – 4y" – 5y' = 9+ 5z, y(0) = 0, y' =…

A: (b) Given ODE: y'''-4y''-5y'=9+5x with initial value conditions y0=0, y'0=0, y''0=4. As per company…

Q: c) Mr Jason deposited $5000 into an account paying 6% annual interest compounded monthly, how long…

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Q: f you cannot see the question, hral Is each statement true or false? deC) b) The first-order…

A: we have to use following relation between function and its derivatives  * when f'(x) &gt;0 =&gt;…

Q: 3. The table below shows the highest daily temperatures (in degrees Fahrenheit) averaged over the…

A: We will use the basic knowledge of trigonometry and the system of linear equations to answer this…

Q: paper 2 4. INDICES AND SURL 2019 N FUNCTIONS + INDICES AND SURDS Q2 Do not use a calculator in this…

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Q: f Loeig)= by? Iny). por yso Determine the partial der Ivatives df, de , deAPc Ond show that d²f = af…

A: The solution is given as

Q: Derivatives of Algebraic Functions Directions: Prove the following statements. 13x + 20x* 2Vx3 +2…

A: Using the product rule of derivative, it can be written that: f·g'=f '·g+f·g'.

Q: 25 s3(s? + 4s + 5)

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Q: 3. The table below shows the highest daily temperatures (in degrees Fahrenheit) averaged over the…

A: As per the question we are given a data table of the avarage monthly temperature (y1) over the…

Q: Determine whether the equation is exact. If it is then solvė it oy-7 In y 3)dt= 0 Select the cortect…

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Q: (*) 3. Let 2 = {A, |n = 1, 2, 3, ...}, where A, Find UN and N2, then !! %3D prove your conjecture.

A: We solve this problem using the basic properties of union and intersection. Also some basic steps of…

Q: Solve for Y(s), the Laplace transform of the solution y(t) to the initial value problem below y+8y…

A: Laplace transform of the differential equation

Q: 3. True or false? If a number is divisible by both 3 and 9, then is must be divisible by 27.

A: Solution

Q: Let f be an arithmetical function such that f(n) > 0 for all n. Let a(n) be arithmetical function…

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Q: f6) = #(1-|). f(x) -L < x < L

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Q: For the initial value problems (a) and (b) fill in (by hand) the representative slopes to visualize…

A: We will find equilibrium point and then sign of slope for different region to draw the slope field…

Q: Civen tz f(x,y) = J 36-9x=y

A: If the graph of z=f(x,y) is sliced by a plane: z=c, then the two dimensional cross-section obtained…

Q: 12- (a) Find the solution ( 5) to the following syStem Of inear equations 3x + 24 t 2z = 5 uy+4z =3…

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Q: - deter mine the Value of I 206 go +复x4

A: We have x+1x2=3 This can be written as:…

Q: ><y<1} The closure of the set E=. a) b) E = c) E=[0,1] d) E=(0,1)

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Q: Find the solution(s) to the following system of linear equations: -3r + 2y + 2z = 5, - 3, —х — 4у +…

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

Q: Calculate the power series solution of the differential equation of y'- y=e* up to the five terms.

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Q: 1. Obtain the PCNF and PDNF of the following proposition: (p – (q ar)) ^ (~p → (~q ^ ~r)) without…

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Q: Let A and B be any two subsets of a metric space (X, d). Then (1) A is a closed set. (2) If AC B,…

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

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A: Parametric equation of line passing through  (0, 1) and (2,0) x(t) = 0 + t( 2-0)= 2t y(t) = 1…