Find a formula for the nth term of the sequence. - 1, 4, - 9, 16, -25, .. Determine the sequence's formula in terms of n. a, = n21

Q: The power series representation of 1 f (x) = 5x +4 is: O 5 25 125 x+... 256 4 16 64 25 125 x++...…

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Q: ||1+ Vx dx

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Q: (b) Find the values of a and b so that the function f(x) = x² + ax + b has a local maximum at the…

A: Given Data: fx=x2+ax+b

Q: Evaluate the integral. (2 4y2 – 7y – 12 J. yớ + 2)y – 3)*

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Q: Evaluate the following antiderivative: | coth(x)(7n(sinh? x ) + tanh? x) dx

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Q: 00 5 converges or diverges. If it converges, find its sum. 3m Determine whether the series > m= 2…

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Q: Q1: To integratef 6x + 8 dx we substitute a)x = sec 0 + 3 b) x = tan 0 + 3 c)x sec 0-3 d) x 3sec 0…

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Q: 3x5 dx - x3

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Q: (iv) 15-22 dr. u = (v) S 15 · T/9 – x² dx. 9-z (vi) J +15 da. u=

A: iv) 15x2/sqrt(9-x2) v) 15 pi sqrt(9-x2) vi) 9x/(x2+15).

Q: Evaluate: 1) [x.e*c

A: We will solve the integration using integration by parts.

Q: parhod derivohve of 4,5 43 6- 13

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Q: (b) Find the values of a and b so that the function f(x) = x² + ax + b has a local maximum at the…

A: Given: We have the local maximum at the point (7, -6). So, we must have f'(7)=0. Here, f'(x) =…

Q: 프-3r-dx= a) 클m3x + 21+ tanx + C b)습 미3x + 21-tan'x + C Q13:J +1)(3r+2) d)흘 I미3x + 21+ tanx + C -1…

A: The integration of the integral is  (2x2-3x) /[(x2+1)(3x+2)].

Q: The partial sum 1 +7+ 13 + .+ 175 equals Question Help: DVideo MMessage instructor Submit Question

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Q: Assuming that out of 200 documents, 40 documents are relevant. A search engine returns 30 documents,…

A: Number of relevant items retrieved =12Total number of relevant items = 40

Q: Calculate the trapezoid approximation of o xdx using four subintervals. O T5 = 21.52 O T5 - 23.25 T5…

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Q: 6 I invest a sum of money at a nominal rate of 6% per year. Find the effective yearly interest rate…

A: Given query is to find effective interest rate.

Q: Trigo nometic substimhon - x"

A: A detailed solution is given below.

Q: Rationalize the denominator. Vx - 9 6/x

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Q: Fill in the blanks: Answer only no need explanation. 1. The derivative of a constant ______ 2. The…

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Q: 29 – 44 dy 2+ 49 с.

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Q: Consider a ladder sliding down a wall as in the figure. The variable a is the length of the ladder.…

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Q: Given: points A (3, 1, 6), B (5, -1, -2), and C (1, -3, 2) 1. Show that A, B, and C form the…

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Q: In a race, Molly starts running from rest at a constant acceleration of 3 m/s. She is running in a…

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Q: Enclosing an Area Patricia wishes to have a rectangular garden in her backyard. She has 64 ft of…

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Q: 12 dx Jx3 – 3x2

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Q: Find the Taylor series generated by f at x= a. (-1)"n(x - 6)" OA. E 6*1 (-1)"(n+ 1)(x- 6)" O B. E…

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Q: (iii) Extremum point(s), (iv) The interval of concavity, (v) Inflection point.

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Q: Q3: A. By power series, prove that: d Cosx = -sinx dx B. Find the value of x for which Inx + (Inx)²…

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Q: d) Find the inverse : y = (x + 2)2

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Q: Find the linearization L(x.y) of the function at each point. f(x,y) = x2 + y2 + 1 а. (3,2) b. (2,2)…

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Q: ∫x+2x√3−6x32x  dx∫x+2x3−6x32x  dx = ∫3sinh(lnx2)  dx∫3sinh⁡(ln⁡x2)  dx =  ∫69+x2  dx∫69+x2  dx =

A: As per bartleby guidelines we only give first three question answers.

Q: 2. If the acceleration function of a certain particle is given by a(t) the velocity function…

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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: 12. Use words to describe the sequence of transformations. Do not graph. f(x)=-4 3x+9 -6 2.

A: Transformation of function -4123x+9-6:

Q: ley'z ds, Cis the line segment from (3, 1, 2) to (1, 2, 5)

A: Given ∫c y2z ds Where c is the line segment from (3,1,2) to (1,2,5) Parameterize the line  r(t) =…

Q: What are the two values of k closest to - 4 for which S, sin? (x + 4) – cos2 (x + 4) dx has a value…

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Q: dy By using implicit differentiation, find dx for xy + e* = sin(x+1). (x.y)-(1,0)

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Q: (a) Use the Second Derivative Test to find the local extreme values of the function f(x) = (x³ –…

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Q: Find all the local maxima, local minima, and saddle points of the function. f(x,y) = e 2x2 + y? - 8x…

A: To find out all the local maximum, local minimum and saddle points.

Q: 2. Find the second derivative for the following set of parametric equations. = t° – 4t3 y = t?

A: We have to find the second derivative of the given equation.

Q: 3. Consider the vector field F(x, y) = (2xy, x² – sin y). Evaluate %3D F. ds where C is the curve…

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Q: Use the transformation u = 3x + 2y, v =x+ 3y to evaluate the given integral for the region R bounded…

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Q: | csc(cot r) + cos? sin? dx

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Q: dx 2+

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Q: C Fnd the firet order parho derivohve of 4.5 f(x,y,2): W y-16y²23+ 43x hCs, t) =° t*In ts) + 9. 1. =…

A: Given

Q: Pr. #3) Prove that the limit does not exist. cos(4ry)- 1 lim (x.v)-(0,0) 2r + 3y4

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Q: Use any method to determine if the series converges or diverges. Give reasons for your answer. - 14n…

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Q: dy dx Jo 17 /289-: Change the Cartesian integral dy dx into an equivalent polar integral. Then…

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Q: 4. § 12×+1dx =. 5. S =dx= -4 %3D . S-3x-1dx vie 6.

A: LetI=∫ 12x+1dxI=∫ 12x.121dxI=∫ 12x· 12dxTake the constant outI=12·∫ 12xdxWe know that…