Evaluate the following integral using partial fractions: 1 (x² + 1)(x² + 4)

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A: We can find the area as below.

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Q: this

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Q: sin -x/3) dx xp. Evaluate the integral| 19-x sin(x/3)dx -1 dp, %3D X-6/ 9-X

A: We have to find integral

Q: Evaluate the following integral using partial fractions: 2x2 +1 dx J(x – 1)(x – 2)(x – 3) -

A: Given: I=∫2x2+1x-1x-2x-3dx   We know that; ∫1ax+bdx=1alnax+b+C And ∫a·fxdx=a·∫fxdx ; where a is cons...

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A: Here we have to use linear approximation formula. 

Q: (x +1)" 2" (n+1)

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Q: Differentiate the following 1. g(x) = x³ cosx 2. g(x) = 4 sec x + tan x 6. h(x) = 5x sin-x 7. h(x) =...

A: 1) g(x)=x3cosxDifferentiateg'(x)=3x2cosx-x3sinx2) g(x)=4secx+tanxDifferentiateg'(x)=4secx.tanx+sec2x...

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Q: Find the directional derivatives of f(x,y,z) = x² y³ – y³z³ + x* in the direction of r = 2i– k, and ...

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Q: Apply the limit laws and evaluate. If your answer is "DOES NOT EXIST" please type DNE. (2 points eac...

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Q: flying horizontally at an altitude of 1 mile and a speed of 480 mi/h passes directly over a radar st...

A: Topic:- application of derivatives

Q: Represent the function 5 In(10 – x) as a power series (Maclaurin series) f(x) = L Cnt" n=0 Co C1 C2 ...

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Q: S cot5xdx S sin³ (2x)cos²(2x)dx 3

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Q: Obtain the general solution. 4y dx *-y *+y OC- y? + 2xy - x² OC = 2y + xy -x2 OC- y? + 2xy + x² OC -...

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Q: Find all the 1st order derivatives of the function f (x,y) = x2y Part 2) Find all the 2nd order part...

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Q: Evaluate the following integral using partial fractions: 2x2 + 1 (x – 1)(x - 2)(x - 3)

A: Topic:- integration

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Q: Use implicit differentiation to find an equation of the tangent line to the curve at the given point...

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Q: Let f(x, y) = xe*-y and P = (11, 121). Calculate || V fp||. (Express numbers in exact form. Use symb...

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Q: If. the.work.required to stretch a spring 3 ft beyond its natural length is 9 ft-lb, how much work i...

A: We have the relation,   Work = ∫abfdx Where f is the force and dx is the distance. According to Hook...

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A: The graph of the function is fx=13x over the interval 2,6

Q: h of the following functions, find the indicated derivative using the de x + cos(3nx) '; f'(1) x2

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Q: Calculate M, for f(x) = 6 · In(æ³) over [1, 2]. M6 ||

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Q: A. y II

A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart...

Q: (2) The graph of f(x) = is the transformation of the graph of y = -'x shifted (A) 2-units left and 3...

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Q: Evaluate the following integral by changing the order of integration: S,2 Vx sin x dx dy y2

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Q: Evaluate the integral. 3* dx 3* +4 Solution:

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Q: 2 4 | 6x V1+4x dx

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Q: q1

A: We have to find out Eigen values

Q: ja2x* +x-a))dx = 24, 3. If find the value of a constant.

A: Here, given that: ∫026(2x2+x-a)dx=24⇒∫02(2x2+x-a)dx=246⇒∫02(2x2+x-a)dx=4...(1)

Q: A particle moves according to a law of motion s = f(t) = t3 - 15t2 + 72t, t2 0, where t is measured ...

A: Solution

Q: Find the radius and interval of convergence of Radius = 0, Interval = empty set >n!æ" . Radius = 0, ...

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Q: Find the domain and range of the function h(x, y) = 3\/3y – 12x². %3D

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Q: Find f'(x) and f'(c). Function Value of c x2 - 9 f(x) = c = 1 X - 9 f'(x) f'(c)

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Q: y(x) =x' (2x – r²)

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Q: For a Taylor series to exist and give the exact value of f (x), which of the following must be true?...

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Q: Explain why the function is differentiable at the given point. 4x f(x, y) = y + sin (0, 6) The parti...

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Q: -IT 2.

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Q: If xy² – y3 = 5, find y'. y' =

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Q: 7/2 r = 6 cos 20 4 2 -4 -2 2 4 -2 -4

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Q: Numbers

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Q: D. Differentiate the following. f(x) = 4x5 - 5x +x +8 g(x) = * --*+x' + v2 c. h(x) = V9x° + V7x7 + V...

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Q: df (x) 7) The graph below represents dx y 5 a) Find the intervals of increase f(x) b) the intervals ...

A: This problem very fundamental for understanding of application of derivative:monotonicty and concavi...