1Evaluate the ff. integrals using either integration by pants, trigonometric integrals , trig on o mctric Sulastitution or partial fractions' a Sx²e*dx b. x²-9 ベ-1)(x+3) dx c. S(4+x*) *dx

Q: tan- (n) Σ Consider the series 1+ n2 n=1 Show that the given satisfies the condition of integral…

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Q: Consider h(x)= {3x^2 +1, if x3. What is h'(3)?

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Q: 4x + 1 dx Jx3 + 3x2 - 6х -36 2.

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Q: ] Using the alternating test, determine whether it converges or diverges

A: Answer and explanation is given below...

Q: Given the series, is it convergent or divergent? (5-4(In n))" %3D2 3n (V5-In n)"

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Q: Find the general solution of the given system. 12 -13 X' = 13 -12 X(t) =

A: We have to find general solution.

Q: . Find the sum of the following convergent series. Σ 00 3n+1 a. 6n-1 n=0

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Q: -+inf In(tan¯1x) 1+x2 1

A: ∫1∞ln(arctan(x)1+x2dxSubstiute u=arctan(x)→dudx=11+x2→dx=(x2+1)du=∫ln(u)duIntegrate by parts…

Q: Which integral that cannot be solved by the substitution method? Integral mana yang tidak dapat…

A: Which of the integral is not solved by substitution.

Q: Find the derivative. f(x) = 2^x {ln[cot(x)]}^2

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Q: Vy x+y Q3) Evaluate triple integral SN S dz dx dy. x-y

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Q: 2. Use integration by parts to evaluate the following. (a) Sx tan- x dx

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Q: C.) approximate derivative; 5.) y = 2x 6.) y = x +34x + 4000

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

Q: Use polar coordinates to evaluate sin (a² + y²)³ dA, R

A: We have to find value of given double integration

Q: Show that the lines L1 : x = 4 – t, y = 2t, z = :5+t and L2 : x = 1 + 4t, y = 3 – 8t, z = 5 – 4t are…

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Q: Find f(100)(x) if f(r) = (x + 2)100. a. 0 c. 100! = 100 x 99 x 98 x 97 x ... x 2 x 1 b. 100 d.…

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Q: VIII. Use the 3rd Degree Maclaurin polynomial for g(x) = x COS to approximate the value of 0.2…

A: Third degree Maclaurin polynomial of a function f(x) is given by,…

Q: 4. A1 y = 2x 2+ A1+ A2 = A3 1+ y= x2 482

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Q: A box is designed so that 4 cans of soup fit tightly into the box, as shown below. ABLE VEGETABLE…

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Q: Find the complete solution of the differential equation using separation of variables 2х + 2ху* y +…

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Q: Solve for the following integral: 1 -dx (e2x – 4)5/2

A: I=∫1(e2x-4)52  dxu=-2xdx=-12 duI=-12 ∫due-u-452v=e-u −4dv=-e-u du-dv(v+4)=duI=12∫1v52 (v+4) dv

Q: The region R is bounded by the curve with equation y = sin 2x, the x-axis and the lines TT x = 0 and…

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Q: | 3xV3x2 + 4 dx = -. 2 (3x2 + 4)V3x² + 4 + c 3 1. O -;(3x? + 4)V3x2+4 + c 2. O 1 (3x² + 4)v3x² + 4 +…

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Q: 2n + 1 n=1

A: We have to check sequence convergence.

Q: Q: Evaluate the following integrals: (10 dt, 10x dt 1. 5t re dx 2. J0 x(Inx)?

A: Question 1,Given,           ∫510dtt+∫5x10xdtt

Q: Is the vector projection of B onto A, perpendicular to B? Is the angle between projAB and the vector…

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Q: 2-x Q1) Evaluate the integral S* dy dx using polar coordinate

A: Given,According to question,Given integral,Let I = ∫01∫x2-x dy dx

Q: 1. A certain object moves in a region of space defined by the following parametric equation: x(t) =…

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Q: Given the integral of S cos² x dx,

A: O integrate the given function.

Q: Find the area of the following regions. Graph the function and indicate the region in question: 2)…

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Q: Using the squeeze theorem, find the value of lim,0 x² sin=) O 1 O -1 O does not exist

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Q: 6. Find the surface area generated by revolving the curve x = 5 cos' t, y = 5 sin' t, 0sts, about…

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Q: +0 (-1)m cos(b) = S-1)" -b2m (2m)! for all be R m=0 Given the integral of J cos² x dx, express it as…

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Q: +o0 In(tan -1 x) dx 1+x2 1

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Q: Using homogenous differential equation determine the particular solution of

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Q: Evaluate: x2 1. dx (x²–25)7 5

A: LetI=∫x2x2-2552dxI=∫1x2-2552x2dxApply integration by…

Q: Evaluate: /4 * 2 sin-1 (플)-zv4-H + C A | f (x) = (В f (x) = 4 sin- (5) + xV4 – a² + C © f (2) = 2…

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Q: Determine the third degree Maclaurin polynomial of f(x) = tan 3x. Use this to approximate the…

A: The given function is; f(x)=tan(3x).

Q: TOPIC: Partial Fraction Decomposition 1. J: 2х3 —х2+2х-2 dx (х2-2х+2)x2

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Q: check if the series below is convergent or divergent, thanks!

A: This question can be solved using the concept of alternating series test.

Q: Solve for the general solution of the following differential equation and determine whether it is…

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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: п(х-2)" Consider the power series 3" (2п-1)3 n=1 Show that the power series converges when x = 5.…

A: the given series is n(x-2)n/[3n(2n-1)3].

Q: Using exact differential equation, determine the solution of

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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: (cos2y — Зx? у?)dx + (сos2y — 2xsin2y — 2x3y)dy %3D0 - |

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Q: 2 [ (e² + 1)² dx et

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Q: 1 III. Consider an 1 for n eN = {1, 2, 3, ...}. 2n + 1 2n + 3 Find a general formula for the kth…

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Q: 4 xp£

A: We have to find the integral.

Q: Q4) Find plane area inside the polar function r 2 and outside the polar function sin -0) +1 in first…

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