Use syntheti¿ division to firid fiz) in f(x) = -x+5x²-7x+1

Q: Use logs and implicit differentiaton to prove (root(x))' = 0.5x^(-0.5)

A: Let y = √x Take log to the base e, i.e. natural log, i.e ln on both the sides, ln(y) = ln(√x) =…

Q: Find the fourier expansion for the function whose definition - - <x <- 2 x, - 2 (x) 0, <x< 2 2

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Q: Evaluate the limit by rationalizing the numerator. Vx + 6 - 3 limr3 x2 - 5x +6

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Q: Use Residue theorem to evaluate dx - x2- 8x+ 17 00

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Q: Evaluate integral of interval 1, 1/2 of (x-3 -8) d x

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Q: rivial of

A: To find the non trivial of Z8 as,

Q: x-3(x-1 + x)²dx

A: Given, ∫x-3x-1+x2dx It is required to evaluate the integral.

Q: Use Residue theorem to evaluate dx x²-8x+ 17 00

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Q: 8(x – a) + 8(x + a)

A: Topic:- calculus

Q: Use Residue theorem to evaluate dx - x2- 8x+ 17 00 8.

A: First we find singular points then we find residues.

Q: Show that, cosh-1 x = In (x + /x² – 1)|

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Q: Let f(x) = y = 4x² In(). Differentiate y = 4x2 In() with respect to x and simplify. + 4x2 )(()이) -A…

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Q: Why are special methods, such as l’Hôpital’s Rule, needed to evaluate indeterminate forms (as…

A: l’Hôpital’s Rule are needed to evaluate indeterminate forms

Q: Express f(x) by the Fourier integral where f(x) = - 2, -3< * < 3 otherwise. %3D

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Q: Perform long division on the integrand, write the proper fraction as a sum of partial fractions, and…

A: Given,          ∫7x3-4x+2x3-x2dx

Q: (x-1)?

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Q: evaluate using method of interse trig function 1 17-257² dt

A: The given integral is ∫11-25t2dt. Evaluate the integral.

Q: Evaluate the integral ſ 2x²Vx³ + 2. Show all steps.

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Q: Evaluate the integral: (x-1)?

A: Given, ∫02(x-1)e(x-1)2dx To evaluate the integral.

Q: Prove that 1- coshx=In(x+ -x=In(x + Vx² -1 |

A: Since you have asked multiple question, as per our guidelines we are supposed to answer only one…

Q: Evaluate the integral using integration of rational fractions: 10dx 4x3 – 4x2 + 5x -

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Q: Evaluate the integral f(16x3 + 4x³)dx

A: To evaluate the integral: ∫16x3+4x3dx Use the formula: ∫xndx=xn+1n+1+C, where n≠1

Q: Does local extrenum of x(sqrt(4))- x^2 exist?

A: Given function is: f(x) = x . {sqrt (4)} - x^2 f(x) = 2x - x^2 ; [consider the positive value of…

Q: find integral  sqrt ( x2 - 9 )/ x  3dx

A: We have to evaluate integral of    x2-9x3

Q: Verify Mean Value Theorem for the function 3x² – 4x + 5 in [-1,1]

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Q: is the net signed area between f(x)=2x+2 and the x-

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Q: Evaluate the integral. 9x2 - 100x - 100 dr - x3 - 100x NOTE: Fnter the er amoa on

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Q: Use canine friendly methods to compute the integral da. Vz(1-2)

A: Let I be given byI=∫01x4x1-xdxlet C be the classical dog bone contour around [0,1] in the complex…

Q: Perform Bisection method and False Position method to Evaluate the f(x) = e^-x -x

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Q: Evaluate the indefinite integral SV1-9x²dx [Hint: use a trig substitution.]

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Q: 2. Use Theorem 4 to evaluate (3x +2x2) dx

A: Given ∫01 (3x+2x2)We know that ∫xn=xn+1n+1+C

Q: - use the Cauchy Residue Theorem to integrate the given function around the

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Q: Find Newton’s polynomial that interpolates f(x) = x1 at x = 1, x=2,x=4,andx=5.…

A: Since, function is not clear so we assume fx=1x. We have to find the Newton's polynomial that…

Q: Express x8 - x as a product of irreducibles over Z2. Please be clear, correct and legible. Thank…

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Q: Does relative extrenum of x(sqrt(4-x^2) exist?

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Q: Use Bisection method to solve (x - 2)¯ - In (x) = 0, [1, 2]

A: Please refer to the image below

Q: sec 2x CSC 2%

A: Solution: Consider the given integral: Now, rewrite the integral: Let u = cos 2x

Q: 3)(2x-ズ) ax

A: First I have split the integral in two parts then just use the rule of integral and find the…

Q: Use Bisection method to find the root of f(x) = x³ – 10x² + 5 = 0 that lies in the interval (0.6,…

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Q: Express x8. -x over Q[æ] and over F2[x] as a product of irreducible

A: Let f(x) = x8 — x. Over Q,f(x) = x(x7 — 1) = xϕ1xϕ7x=xx-11+x+...+x6 Note that  ϕ1x and ϕ7x are…

Q: section method to

A: Given,         f(x)=x-cos(x);     0, π

Q: 3x* +5x-8 lim 5x' – 7x+2

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Q: Evaluate the integral by first performing long division on the integrand and then writing the proper…

A: ∫x4x2-4dx take long division

Q: # (u²-1)4 (u² + 1)4 du

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Q: Show that cothx x+1 In X-1,

A: Solution

Q: Find the root of f(x)=(x^2)-5, in interval [0,4] by using bisection method.

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Q: 3. Show that 5 x + 7 is a continuous fimction

A: Let, f(x) = 5x+7 be defined over R, the set of all real numbers. Choose an arbitrary point c in R.…