+o0 (-1)*n" sin" () Σ 2n n=1

Q: Solve [15x/1- xdx . S 3xV3x2 + 4 dx = --

A: 1) the given integral is 15x sqrt(1-x). 2) the given integral is 3x sqrt(3x2+4).

Q: Find the area ef"l fhe Shaded reghon a/2

A: I am going to solve the given problem by using some simple calculus to get the required result of…

Q: II. Consider the sequence (n + 2)! n=1 a.) Show that the given sequence is monotone. b.) Use the…

A: Given

Q: 3" en – 2n n=1

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Q: 1 Find the sum of the following convergent series: > L n? – 3n + 2 - n=3

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Q: Find y' if 3x2- (ry?) = 2y.

A: y' = ? 3x2 -(xy2)1/2 = 2y3 3x2 - x1/2y = 2y3 differentiate with respect to x 6x - y/2x - xdy/dx =…

Q: 2.x3 – x² + 2x – 2 dx x² (x² – 2x + 2) -

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Q: x* Find the exact length of the curve y =- 1 2<x<4.Show All Work and Give Answer In Simplest Form.…

A: We have to find length of a curve for the given interval.

Q: Why do we most often settle for just answering if a series converges instead of trying to find its…

A: This is a problem related to series and sum calculations. Based on the general concepts we will…

Q: Calculate the moments My and My and the center of mass of a lamina with the given density (p = 3)…

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Q: Using exact differential equation, determine the solution of: dy y dx 2x %3 Зу? — 2 when y 1 and x =…

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Q: 4 xp£

A: We have to find the integral.

Q: ********** . ...... Analyze and sketch a graph of the function. Find any intercepts, relative…

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Q: A true statement for the function f(x)=2x³-3x²+10 is.... Pernyataan yang benar dibawah ini untuk…

A: The given function is: f(x)=2x3-3x2+10 Now, f'(x)=2(3x2)-3(2x)=6x2-6x=6x(x-1)

Q: Evaluate the following sum of iterated double integrals: r4-2y eAr-r² dx dy 2 2y dx dy +

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Q: Find the sum of the given convergent series. > [tan-1(2n – 1) – tan-1(2n + 3)] n=0

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Q: Consider the parallelepiped with adjacent edges u = 3i + 3j + k v = i+j+ 8k w = i+ 9j + 5k V Find…

A: Given;  u=3i+3j+k v=i+j+8k w=i+9j+5k.

Q: VII. Let f(x) = %3D 1– 3x 1. Find a power series representation for f(x) for all r € 2. By first…

A: Solution is given below:

Q: 678 COS (x³) dx 3

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Q: : s ech[In cosx]tanx dx Evaluate: A None - 2 tan-1(cosx) + C 2 tan -1(e cosx) + C CoSx (D - 2 tan…

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Q: If substitution technique is used to solve the integral [(12.x+3x* )(10x² +x³ – 2)° dx then the…

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Q: Find the value of 7x²e-3 Determine whether ) (7n’e- ) n=1 Enter C if series is convergent, D if…

A: Let's find.

Q: f(x) = -x^2 + x + 20 and g(x) = x^2 - 5x . Compute the area of the region enclosed  by the graphs of…

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Q: Find the exact value of the indicated trigonometric function of 0. 4 31) tan 0 = -, 0 in quadrant II…

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Q: dx 3 x² (9x²-4) 7

A: We have to use properties of integration to solve the question

Q: 3). 5 dx =

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Q: Q3) Evaluate triple integral N S dz dx dy . x-y

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Q: Find sets of parametric equations and symmetric equations of the line that passes through the given…

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Q: бх — 8г2 — 5 dx (2л — 1)(4г2 + 1) -

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Q: 0 e1/x dx х2

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Q: Find the sum of the convergent series tan - ( m til tan M=1

A: This is a telescoping series.  Whose sum is  2/π

Q: x2 — бх + 9 dx V6x – x2

A: We have to find value of given Integral

Q: lim (sin r)tan z T/2

A: Given problem :- Identify the indeterminate form and evaluate limx→π-2sinxtanx

Q: 3/2 5. Find the exact area of the surface obtained by rotating the curve x =- Show All Work and Give…

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Q: Calculate the following limit: lim,→4 4 x-4 O -1/16 O4 O -4 O does not exist

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Q: Evaluate the integral cos x 1- sin z dx .

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Q: log;X + (Arcsin5x)³ b. w = + (Arcsin5x)³

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Q: Find the general solution of the given system. dx бх — у dt dy = 5x + 2y dt (x(t), y(t)) =

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Q: 9. x=t² +1, y = 3t² + 2t . d y b) Find dx? Show All Work and Give Answer In Simplest Form.

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Q: Use trigonometric substitution if possible dx x? (9x2 – 4)2

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Q: . Evaluate the integral. Shade the region whose net area you have found. 3 Ax) S(-x+3x* + 1) dx =

A: Given problem:-

Q: 3 < x < 2/3 < x < 3/2

A: We have to choose the correct option from the given options according to the given information

Q: +00 (4-х)^/п+5 4. Consider the power series 9n-7n n=1 а. Use Limit Comparison Test to show that the…

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Q: A closed rectangular bOX with a volume of 16ft° is made from two kinds of materials. The top and…

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Q: V3/2 1 dx%3D 6). V1- x 1/2

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Q: (x² + 2x) cos(2x) d»

A: Given problem:- ∫ (x2 +2x)cos(2x) dx

Q: I. Evaluate the following integrals. 1 1. d.x " J r(9 – In² r}5/2"

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Q: 1 Given that 1 1 with > x" with convergence in (-1, 1), find the power series for - r. n=0 center 3.…

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Q: 36) y = 2 sin x - 4 10+y 8-

A: to find the differentiation of given function.

Q: (Vian tan³ x + 1) sec" x dx

A: