(-1)" x2n+1 En=0 (2n+1)! Given: sin x = for x ER Determine the exact value of the sum Σ (-1)"(2n + 1) 4" (2n + 1)! n=0

Q: 512x 1-x -3 - =—1 find volue of Σ(x²)"=? n=1

A: Given that the equation 512x1-x-3=-1   .

Q: lim (1 – 3" =e3 n - n + 00 Select one: True O False

A: Hence the statement is false . Bcoz the value of above limit is 2•5

Q: Evaluate ∞ ∑  4(1/2)ˆ(x-1) x=2

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Q: x2 (b) x x4 2! 3! 4! 5! +

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Q: S (s² + 100) (s − 8) } Evaluate ¹{.

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Q: Evaluate O x3+4x²+ 6x Select the correct answer below: -1 2² ) ) + 0 O (2 In [x]-In (x² + 4x+6) +…

A: Given thattaking firstly using the partial fraction decompositionon comparing the like terms

Q: Given: sinx = (-1)" (2п+1)! x2п+1for x € R n=0 Compute the exact value of the sum 0-1)"(2n+1) „2n+…

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Q: (-1)"n2n+1 n=0 32n-1(2n+ 1)! The sum of the series is 3 18 O 9/3 1 18 tan() 3 9 tan Click Save and…

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Q: 2 DO NOT USE A CALCULATOR IN THIS QUESTION. Find the positive solution of the equation (5+4/7)x²…

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Q: dthe She (5y-3)

A: We have to find (5y - 3)2

Q: dæ - x² – 10a – 21 -x – 3 - In x + 7 -æ – 3 -In +C +C x + 7 A x + 7 æ + 7 -In -x - 3 +C -In -x – 3…

A: Here we will solve the given intigral,

Q: Write the sums in expanded form: 3 k +1 (a) (b) sin (i + 2) (c) (d) E(-1)'iæ*- COS i 2k – 1 k=1 -…

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Q: Express in lowest terms. x+ x* x - x+ 1 ) 1+ x? O x(x + 1)

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Q: show that 11 1+ 1 n-1 1 n(ā-μο)2 Σ=1(xi-x)2 n/2 n(ā – μο)2 Σ=1(α; - z)2 (xi

A: We need to prove that:

Q: The infinite sum 0-1 Ⓒtan(+) tan (2) © tan ( ) 1(4)¹ 3(4)³ + - ty 5(4)5 +... is equal to

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Q: Simplify the sums given below. (1) + ¹ (1) + ¹² (2²) 4n ™ ¹″ (3) − 4¹ -¹ (1²) + 4²¹²¹² ( 2 ) + . . .…

A: Here we have to simplify the given sums by using the Binomial theorem. The Binomial theorem is given…

Q: (a) Write using summation notation: 1 +1 + 1 + 32 + 1 3n (b) Transform the summation by making the…

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Q: 1. Find the sum: ( a) Σ (3i-2) (b) Ej-s 70 2 =3 jG-2) (C) Σ25, 2i(i – 1)

A: To find the sum of the given finite series. Note that: ∑i=1n1=n∑i=1ni=n(n+1)2∑i=1ni2=n(n+1)(2n+1)6

Q: Q.4) Find the value of Sigma (d=sum of student id + 22, and c=12) 4c(d + x)(7c* +2cz +9z*) ((d +x)*…

A: As the student ID is not provided, I assume the sum of the digits are 10 (say). Then d=10+22=32 and…

Q: dx ** Evaluate x(x + 1) 1 (A In 4 (B B In5 none of these D In 4 1 E

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Q: (1) (a) show that 21 divides 4+1 +52n-1 for n ≥ 1 (b) Let T₁ = 3 Tn Tn-1+2" for n ≥ 2. = Show that T…

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Q: 32/3 x72(3 – x32)*. Evaluate 02 (39) В (5, 3) 02 (35) р (5, 3) о(3) в (3, 5) 2²p () 3

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Q: If I = may be Evaluate I 20 do 1-2p000 + p² written using show that it 3=eja dz (1-P3)(3-P) of the…

A: Let the given integral is  --------- (1)            For evaluate the above integral consider the…

Q: (z- 1) The residue of f(2) = at z = -9 is -9e9 (z + 9) Select one: O True False

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Q: 5x2 + 13x -dp x³ + 2x² – x – 2 Evaluate: (x + 1)ª(x – 1)³' + C (x+2)² (B None of the choices given…

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Q: The identity formula we have been using is 1/n= 1/(n+1) + 1/n(n+1).  Here is the problem at hand:…

A: We need to use given identity twice to represent the unit fraction  in three term

Q: -16x'y' + 30x°y' +4x²y' factors to -2x'y' (8x+y}(x-2y). True O False

A: The given expression is: -16x4y3+30x3y4+4x2y5

Q: 2-¹ {881 (0 -₁)} = athert sen(8t), (8-8)²+64, What's the value of a*c?

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Q: 23 The value of cot Scot Scott n=1 (a) 23/25 (b) 25/23 (c) 23/24 n 1+ Σ2k k=1 is (d) 24/23

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Q: Which one of the following fractions is NOT an improper fraction? 2x' +x' +1 a. x(x+2)(x-1) x+3 b.…

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Q: 1. 3Y4 + 3Y5 + 3Y6+ ...+ 3Y15 2. (Xg — 4) + (X, — 4) + (Х10 — 4) + (X11 — 4) 3. (X3Y3) + (X4Y4) +…

A: To write in summation notation  1): 3 y4+3y5+.......3y15  2): (X8-4)+(X9-4).........(X11-4)  3):…