A³ f2 = V³ fs 3

Q: Verify the Mean value Theorem for the function f(x) = 2r2 - 8x +6 on [1, 3]

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Q: Let {(=) = In ="(z +2)*(z² + 9)] f'(x) =

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Q: 2. Explain how to use the evaluation part of the Fundamental Theorem of Calculus to compute J", (3x²…

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

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Q: Suppose that | f(z)dz = 2, | f(z)dz = 1, %3D [ 9(2)dz = - 5, | 9(2)dz - 2. Then, | (=) – g(2))dz =

A: Given: ∫25fxdx =2, ∫23fxdx =1, ∫25gxdx =-5, ∫23gxdx =-2 To evaluate:∫35fx-gxdx We know that…

Q: Verify the Mean value Theorem for the function f(x) = 2x2 - 8z +6 on [1, 3]

A: f(x)=2x2-8x+6  on [1,3] conditions of mean value theorem: i) f(x) is continuous at (a,b) ii) f(x) is…

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: Use use Theorem to find 23) fH) = 4+64-3 %3D F(t) = Itet

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Q: 4. Use the Fundamental Theorem of Calculus to evaluate [(-3) -

A: The objective is to find the integral using fundamental theorm.

Q: find the anti- deriva tive of the fun cticn: fcx) = 4 cSca cotx - Secx cot x

A: Derivative of function

Q: Explain how to use the evaluation part of the Fundamental Theorem of Calculus to compute L", (3r² –…

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Q: without using the picture, prove that z^7 + 3z^4 + 0.5 has the same amount of zeroes as f in the…

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Q: 0.2 Differentiate In x+1, with respect to x. x²-x+1

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Q: Compute the subdifferential of f(x): R->R f(x) = x^3 + |x+1| + |2x-1||

A: Solution:Given  f(x)=x3+x+1+2x-1To compute the subdifferential of f(x)

Q: Show that - In(x – V - 1) = In(x + Vr – 1)

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Q: prove using the IVT. √2 exists. Hint: Consider f (x) = x2.

A: we have to show √2 exists. Now let

Q: (a) Prove or disprove: f: Z3 → Zs, [r]3 + [r*]5 is well defined.

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Q: power

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Q: Compute f.F. dr, where F(x, y) = (2+ 12x²,9xy² ) and C is a line segment from (0, 0) to (1,2). (Use…

A: To Determine: Compute ∫cF.dr,where Fx,y=<2+12x2,9xy2> and C is a line segment from 0,0 to 1,2.…

Q: Let fé)--을(t)6. Eveluate f(-8) %3D f68)= ? %31

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Q: Find the number of positive integers less than 1000 that can be expressed as the difference of two…

A: Find the number of positive integers less than 1000 that can be expressed as the difference of two…

Q: Suppose that f(2, 3,1) = 5, fz(2,3,1) = 2, fy(2,3,1) = 3 and f.(2, 3,1) = -1. %3D Then f(1.9, 3.3,…

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Q: Choose all the equivalent expressions for f(x) = (2x +7x² + 2x + 9) ÷ (2x + 3) O f(¤) = (2x + 3) (x²…

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Q: f should be split into two questions because it is unbounded. so can it be reviewed please?

A: As per our guideline, we are supposed to solve only first question. Kindly repost other questions as…

Q: Find f'(1) for f(x) = In(v6x – 3).

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Q: 5. Show that Ax) = Inx² - 1- In/3, if f'(x)= and (2) = 0. x- 1 Justify your answer.

A: To show that f(x)=ln|x²-1|-ln√3

Q: 3. Show that f(2) = (z+ 1)³ – 3z is nowhere analytic.

A: The given function is, fz=z+13-3z The function z is given by, z=x-iy Substitute values in above…

Q: Gven that Pe3 -3 3 f On Compore

A: 3. Given that, P=52337-1, Q=5-31237. (i) Obtain the value of PQ as follows.…

Q: Compute f' (3). f (x) = –3.3x² + 3.9 O f' (3) = –19.8 %3D O f' (3) = –3.3 f' (3) = -15.9 O f' (3) =…

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Q: Use calculus to find the critical number of f(x)= x4/4 - x3/3 -3x2+10

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Q: EER(F}}

A: Introduction - F-test of H0:β1=0consider the hypothesis test H0:β1=0Hα:β1≠0Note that Yi^=b0+b1Xiand…

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: Compute f' (3). f (x) = -3.3x² + 3.9 %3D O f' (3) = –3.3 %3D O f' (3) = –6 %3D fl O f' (3) = –15.9…

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Q: it is unbaised estimated of a Then Show That ta is baised estimated of 02. Theorem:- if

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Q: Proved that cosh fas/ (cashZ+L)

A: To prove :  cosh2z2 = 12cosh (z) + 1

Q: 6 Evaluate f S Suh

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Q: Show that div (r x a) = 0

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Q: Prove that x=0(x)

A: We say that a function f is O(g) if there exist constants M and C>0 such that For all x>M…

Q: 27 Use the Fundamental Theorem of Calculus to evaluate S (Vx2 -) dx. 8.

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Q: Verify the Mean Value Theorem for f(x) = In(6x + 1) on | 0, %3D

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Q: Show that f(x) = x4 − 5x2 + 1 is irreducible in F[x] = Q[x]

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Q: 2 (1 – :-) d.x

A: Given ∫141-2x2dx

Q: (*;)-()0)

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Q: Frngl. prove that x

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Q: Find the interval and radius of conv. of In(1 – x²)

A: The power series representation of given function ln1-x2 is given by: ln1-x2=∑n=1∞-x2nn

Q: Determine the first root of: f (x) = –13 – 20x + 19x2 – 3x³ with False position method. Use initial…

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Q: Prove that V/3 (1-x) (1+2x) 33

A: To Determine :-  ∫01 x13 1- x 231 + 2x  dx  = 2π33

Q: Prove that: 3-4x² dx 4VIn3

A: The given integral is I=∫0∞3-4x2dx. The idea is to evaluate the above integral using gamma function.…