Use the formula for the binomial series: m(m-1)---(m-k+1),k + m(m-1) (1 + x)" = 1+ mx + + %3D ... 2! k! 1+ E: m(m-1).(m-k+1),k 1지 < 1 if k=1 k! to obtain the Maclaurin series for V1 +x. 14..(5k – 6) 5*k! 9. 1+ Σεν k=1 1 I+*+ E(-1y*+14.9 · 14..(5k – 6). k! k=2 :+ E(-1)*+14·9 · 14.--(5k – 6) 5k k! k=2 1 -x + S(–k , 4·9·14..(5k – 6) 5* k! k=2 9. 14..(5k – 6) 1+ >, k! k=1

Q: Find the general term of the sequence, starting with n = 1. Determine whether the sequence converges...

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Q: Evaluate

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A: Question- Find an explicit formula of  an   for the nth term of the geometric sequence whose first t...

Q: Problem 1: Answer each of the following questions. (a) Give the candidate general solution using the...

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Q: A travel agency charges a fixed 5,000 pesos fee for a travel tour with a group of 1 to 5 people and ...

A: Given: - A travel agency charges a fixed 5,000 pesos fee for a travel tour with a group of 1 to 5 pe...

Q: Write the first five terms of the sequence, give the exact answer: +o0 n n+ 19 J. n=1 Determine whet...

A: nn+19n=1∞  

Q: dx xvx*-4

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Q: d) Verify if y = 2e* + x - 1, solves y' = x - y

A: If y=2e-x+x-1, solves y'=x-y

Q: D)

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Q: dx The integral / can be re-written as 1- x (A lim (2 - 2 V1-m ) m-- 00 B lim (-2 + 2 V1–m ) m-- 00 ...

A: ∫-∞0 dx1-x

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A: The given sequence is: an=7n6n2n=1∞

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A: Given query is to find the determinant of the matrix.

Q: Graph the parabola, then label the vertex, axis, and intercepts. 1 Y = --x² + 2x + 4 %3|

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Q: Graph the set of points whose polar coordinates satisfy the equation 0 = r20. 5 Choose the graph tha...

A: Given that polar cuve equation θ=π5,r≥0Solution :π5&lt;π4θ&lt;π4r≥0

Q: Find the derivative of the function y = cot^-1 x2 – cos^-1 x + 1/x – 2 %3D

A: To find the derivative of: y=cot-1(2x)-cos-1x+1x-2...(1) Note that: ddx(cot-1x)=-1x2+1ddx(cos-1x)=-1...

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Q: Find the Taylor polynomials of orders n = 0,1, 2, 3, and 4 about x = x0 and then find the nth Taylor...

A: Solution: 5sin(πx);   x0=132,  n=0,1,2,3,4  

Q: The sum of the series n-16) is: A) 1. B) 2. C) D) E) Diverges.

A: topic - series convergent and divergent

Q: Find dy. y%3Dyx+4

A:

Q: What is the value of the discriminant whose root are real,rational,and equal?

A: Given: - The discriminant whose roots are real, rational, and equal. To find: - The value of the dis...

Q: One of the following series is convergent. A) E-1(-1)" 21 3n+1 100 2n B) E1(-1)" 3n+1 C) (-1)" 100 3...

A: We have to check whether the given series are convergent or not. To check convergence we use Alterna...

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Q: 1. The graph of y=f(x) is drawn below, sketch a graph of y = s"(x).

A: Solution: According to the given graph points A(-1,3),   B(1,-3),   C(2,1) 

Q: Given: -dx. Using u-substitution and transformation of integrand, what is u and du? 3/x - 2x 3 (A) u...

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Q: # m Find Ay and f'(x)Ax. 2. For y f(x)=. x = -1.6, and Ax = 0.1 at x = -16 and Ax = 0.1 (Do not roun...

A: We will find the values of each. 

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Q: Question A potato is launched vertically upward with an initial velocity of 136 ft/s from a potato g...

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Q: Question 3 Determine whether or not each of the following sequences is (i) bounded, (ii) monotone, a...

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Q: Problem 2: A piece of string whose length is given below is cut into two pieces. One piece is used t...

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Q: The integral that represents the arc-length of the curve y = In x, xE [2,3] is: %3D 3 x2+1 dx. Vx2+1...

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Q: A ball is launched vertically upward with a velocity of 256 ft/s, so its position function can be mo...

A: Given that, s(t)=-16t2+256t

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A: Given problem:-

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Q: The region R shown below is bounded by the x-axis, the y-axis, and the curve given by the parametric...

A: We have to write the integral expression

Q: Find the Taylor polynomials of orders n = 0, 1, 2, 3, and 4 about a = x0 and then find the nth Taylo...

A: The formula for the Taylor polynomial of degree n is: pn(x)=f(x0)+f'(x0)1!(x-x0)+f''(x0)2!(x-x0)2+.....

Q: Verify the inverse function theorem of the function y = 4x2 +4x + 9.

A: Solution is given below:

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Q: . Find two positive integers such that the sum of the first number and four times the second number ...

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A: Given series ∑n=1∞(-1)nxnn3n

Q: %3D h that x+3y =16. |=

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Q: S' 2. a Find Ay and f'(x)Ax for y f(x) = 9x°, x= 4, and Ax = 0.04. (Round to four decimal places as ...

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Q: 1. A manufacturer spends z thousand pesos on labor and capital. The number of units of labor obtaine...

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Q: Find Ay and f'(x)Ax for y = f(x) = 3x° x= 2, and Ax = 0.08.

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Q: Find the sum of the series: 6 (n – 2)(n + 1) or conclude that it diverges. A) A B) C) D) 0.

A: option (C)  is correct see below the answer and calculation

Q: The derivative of f(g(x)) equals f'(x) evaluated at multiplied by g'ʻ(x) evaluated at g(x) g'(x) f(x...

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Q: Find the derivative of the function. 7. x3 + 2 y = e

A: Given:         y = e x3+27

Q: 4 Consider dx. Transforming the integrand, the result will be K -, where k is a constant. What is u ...

A: