1. 05x<5 2k ī (x) if (I - x) if sxsI 2 2kx < 1 2

Q: 49. f(x) = alst %3D n=0 Selet ai 50. f(x) = 2 (-1)+1(x – 5)n n5" n=1 * (- 1)n+1(x – 1)"+1

A: f'(x)=∑n=1∞ (-1)n+1n(x-5)n-1n5n      =∑n=1∞ (-1)n+1(x-5)n-15n Apply the ratio test to check the…

Q: 10. Evaluate the integral. dx x²/4 – x²

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Q: a=t). CTaylon Serie) 2-X Ln +x) (MacLurinSeries

A: We need to find the Taylor series of f(x)=12-x at a=1. Taylor series of function fx at a is defined…

Q: 7. Evaluate the Integral S (x + 3) dx

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Q: |(In 6x)2 dx ОА. x(In 6x)2 - x(In 6x) + x + C В. x(In 6x)2 + 2x(In 6x) - 2x + C с. x(In 6x)2 - 2х(In…

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Q: Solve the intial value problem f'(x) = 7x (x6-4) withf (I/6)=0.

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Q: in terva! 3 Find absolute extrema for fCx) = x°-9xャ15x-3 in terval [0.3] Oへ

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Q: 10. f (x) = x² + 4x + 4 Opens up/down:. Vertex: Axis of symmetry: Solution(s): y-int: Domain: Range:

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Q: 5. Evaluate the integral. x+7 (x-6)(r-2)*a

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Q: Find the antiderivative of: xn+1 [(n + 1) In x – 1] if n+ -1 x" In x dx = (n + 1)² 1 (In x)² + C 2…

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Q: Since a certain virus has been contained in Wakanda, researchers has proven that it will be…

A: Given,             Since a certain virus has been contained in Wakanda, researchers have proven that…

Q: 1 Integrate with respect to x. 4+ 25(3x +1)²

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Q: 5 2 +2 ) dx using Estimate I - n = 4 subintervals and (a) Left endpoints. (b) Right endnoints.

A: solution:-I=∫152x+2dx,     n=4f(x)=2x+2∆x=5-14=1(a) Left end pointI=∆xf(1)+f(2)+f(3)+f(4)…

Q: Find g'(3). g(x) = In(1+t) dt In(4) 6ln(10) O In(10) 3

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Q: 6. x³dx = 320, / 2 6. 6. 16, /dx = 4 2 Given / xdx : %| 2 Find the following S (-x³ + 7x – 12) dx 2…

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Q: (−5x+6)(x+4)(x−8) has root(s) at x=

A: Given expression is

Q: 5. Solve: (1 + + In x + dæ = (1 – In x) dy

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Q: (2x+4) + 1 x² +2x- 10 dx = x² (x² + 4x +5) (2x +4) +1) dx- x² + 4x+5, Consider dx evaluate | x² + 4x…

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Q: | Va(In(x))° dr (ax) 1.

A: We find the integration by substitution.

Q: x2-2 x+1 x2 --x-In Ix+11 + C C. + x- In Ix+ 11+C x2 -x + In Ix + 11 + C 2 +x + In Ix+ 11 + C O B

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Q: 1 Find xIn(x15) dr. xln(x!5) 1 а. xIn(x!5) 1 -In] In(x!5) |+ C 15 1 dx = In] x'5 |+ C b. xln(x!5) 1…

A: Use the substitution method and integrate the given expression.

Q: 3. f(x) = -x² +1 Ex)(+x). x2 + x - 6 %3D Holes: Vert. Asy: Hor. Asy:

A: Now plotting the graph of given function we get :

Q: s at x =-1 and x = 2

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Q: 1. Differentiate the following with respect to x: a. y= 5x - + 5Vx + 3p ex + In(x) - 7 (9)

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Q: the integral S(x³ – 2x – 1)e-*+1dx is equal to:

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Q: Evaluate the integral : S 8x2+10x-6 (x-1)(x+1)z dx (2—1)(ӕ+1)? +C

A: Given: ∫8x2+10x-6x-1x+12dx To do: Evaluate the given integral.

Q: de xdx 1. (In* 4x-1) 2. V3x +5 sin 4x de de 4. 9+8cos 2x 3. (5x-3)dr 5. 3x-3x+2 (3-4x)dx 6. TAx…

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Q: 1 if dx =3 then K3D203 Select one: O True O False 03789

A: objective to find the integration.

Q: By= In(Cx-2)

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Q: 5s +1 To determine L-1. |s² – s – 12

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Q: S de x² –2 x+1 A x2 --x - In Ix + 11 + C C x2 +x - In Lx + 11 + C B x² -x + In Lx + 11 + C x2 +x +…

A: Given ∫x2-2x+1dx. The objective is to evaluate the integral.

Q: 2- S5olve X" = LX given u =1

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Q: 8. Compute using the trig. substitution S x2 -dx (1–x²)1/2

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Q: 12. Find the general solution using Reduction of Order: a) y" = 31n x

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Q: (6) Find the indefinite integral (af* -3x +2 Fdx x+1 12x - 22x (bJ -dx 3x* -11x +15 x² + 2x +3 -dx…

A: Note: As per companys policy we should do maximum 3 subparts of a question.So, kindly post the other…

Q: 4. If the secant method is used on f(x) = x^5 +x^3 +3 and if x_(n-2) = 0 and x_(n-1) = 1, what is…

A: The given function is,

Q: 7. Consider the IVP y'=(2x-4)e" with y(5)=0. Verify that y = In(x² – 4x -4) is the solution to the…

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: S x2 +2x-10 (2x+4) + 1 JE + 4x +5) Consider dx = x² (x² + 4x + 5) (2x+4) + 1 dx- x² + 4x +5 dx ,…

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Q: 2. dy axta¹ x-In√x²t)

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Q: solve for x if CDy=4(x-E)

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Q: 3. Find the integral x² +12x +12 dx x' - 4x

A: Given,            ∫x2+12x+12x3-4xdx

Q: −x^2+x+6 has root(s) at x=

A: To find the roots of the given equation.

Q: 6. Evaluate the integral dx (4x2 + 1)(x² + 4)

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Q: 8. The value of the integral 2[x] 1o sulsV ar 3x-[x] dx, where [] denotes the greatest integer 2[x]…

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Q: 8. Evaluate the integrals. * Sx³ (x² + 1)5 dx

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Q: 7. Evaluate the integral x4 6x5 1 dx

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Q: A) Vn +5 B) is larger than Vn + 5 1.

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Q: 2x²-3x + 10 dx (x²+4)2

A: The objective of the question is evaluate the indefinite integral.