Determine the ratio and interval of con (-1)"x" in=0 n6" O R.O.C=6, 1.0.C: x E [-6, 6) R.O.C=1, I.O.C: X E [-1,1)

Q: (a) For f(x) = x² sin(x), find a partition P of [-5, ) such that U(f, P) – L(f, P) < . Note sin() =…

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Q: d) Using Demoivre's theorem, show that, if z = e“, then i(:-" - ") sin no = ne N+ 2

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Q: Let C be the shortest path that connects n to ni and I = [, (sinhz + 1)dz. Then O I=-sinh n+ n(i-1)…

A: Second option is correct answer i . e . I = -1-cosh(π)+π(i-1)

Q: 2 Use the figure to identify all angles between 0 and 2n satisfying the condition csc (0) = -- V3…

A: Given that, There is a figure in which angles are pointed and cosec θ=-23 We have to find the value…

Q: Find y(0), y(1), y(e), y', y", and a formula for y(") where n is a natural number. Use DNE, Does Not…

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Q: Find the values of x in the interval [0, 2π] that satisfy: sin² x-1=0 O x = 0 and x = πT x = TT/4…

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Q: The domain and the range of z=cos-¹(x²-y-3) are represented respectively by OA. D={(x,y) ERXR: x² ≤…

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Q: f(x)=2sin(x)+4cos(x), then f'(x)=? f'(5)=?

A: Given  f(x)=2sin(x)+4cos(x)

Q: 15: Using first principles (by definition), prove thát thể đêrivätive of ä constant is U

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Q: If I, = [x^tan"x dx, Prove that (n+1), + (n-1),,2 ° п 1 %3D 2 n

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Q: Led xe R be such thad Xn→x, show that %3D

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Q: Cannot solve

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Q: 2. Verify that the function satisfies the hypotheses of Rolle's Theorem on the given interval then…

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Q: If X is uniform in the interval [-3,3] compute X(i.e. E{X}) and o² (i.e.E{(X-X)²}).

A: Given that X ~ U[-3,3] to find mean and variance

Q: Functional theory and functional analysis

A: According to the given information it is required to prove that:

Q: Find exact Values for x in the interval 0,360°) that satisfY the equation. 3Sin 2x+2Sinx=|+3cosX

A: Given equation 3sin2x+2sinx=1+3cosx

Q: Find exact Values for x in the interval 0,36O°) that satisfY the equation. 3Sin 2x+25inx=1+3cosx

A: We know that the formula of sin(2x) = 2 sin(x)cos(x).

Q: Given f (x) = |x| for x E [–n, 1] Show that 4 cos(2n – 1)x |x| = 2 E - - - (2п — 1)2 n=1

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Q: the interval [a, b], where c; is any point in the ith s Interval [-3, 3]

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Q: Consider the function f(x) = - cos x + sin? r on the interval 0, |. 2 (a) Find the critical numbers…

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Q: On which interval is the IVP (x sin x)y' + 2y = x +1, y(-5) = 2 guaranteed to have a unique…

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Q: The Ideal Gas Law states that PV = nRT where P is pressure, V is volume, n is the number of moles of…

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Q: By using Rodrigue's formula, prove the following relation Ph+1(x) – Ph-1(x) = (2n + 1) P,(x) 4- %3D

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Q: Find дх (дхду) 6,e at the point(7,), where g(x,y) = cos(y) [sen(x) + xy].

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Q: Find all the joint moments m, n and k = 0,1,.... "nk

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Q: The base of a three-dimensional figure is bound by the graph x = cos(y) + 1 on the interval [-n, r].…

A: Option(2) is correct answer.

Q: What is tanh (Ei) O V3 V3i O 13

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Q: x is the distance 1:- Show that the from morm Il x|l o7 2 to

A: We have to show that x of x is the distance from x to 0 Hence, x can e written as x−0 x=x−0 The…

Q: The area bounded by the curve y = 7x and the lines z= 2 and =9 above the z-aris is O 539.00 square…

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Q: Use the Mean Value Theorem to establish the following inequality | Cos r - cos y S ær – yl, for r, y…

A: As per our Guidelines, we are supposed to answer only one question. Kindly repost other questions as…

Q: 4. Find Rable With respect ho X and X is also iable nith respect b . a ssuming fhat Y is diffrent…

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Q: 5. Use the Mean Value Theorem to establish the following inequality |cos r- cos y < |r – yl, for 1,…

A: According to the guideline we should have been able to solve only first one question at a time

Q: Find the egetion of the tanqent line on the interval (o,5) to co.1, 6.2)

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Q: 16. Find he exact soution on The interval [0,2m] 25in?x ャ Bsinx +3= 0 5sinx t

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Q: Q: Prove that : sin' ne -de = na for all n e N. sin' e

A: solution is given below

Q: Given f(x) = |x| for x € [-n,1]| Show that cos(2n – 1)x |x| 2 \xl = -- - (2n – 1)2 n=1 2.

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Q: The domain and the range of z=cos-¹(x²-y-3) are represented respectively by A. None of the choices…

A: We have to find the domain and range of z = cos-1(x2-y-3).

Q: Ôz Ôz If Z= tan"'(2) -= 0 show that : *-+ y ôx ôy

A: Let us consider function z=f(x,y) Where f is function of x,y. ∂z∂x represents partial derivative of…

Q: Consider (Ru) .f : R->R -3 X3o 3. X70 Prove Pex) is Con tinuos onR-301

A: Given that                                      f:R→Rf(x)=-3; x≤03    ; x&gt;0 we have to prove that…

Q: 10. Find all the values of a in the interval [0, 27] such that f (a,=) - fxx (a,=) = 0 for f(x,y) =…

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Q: 8.Prove the following relationships: a) I(X,Y)=H(X)-HOX/Y)

A: Solution

Q: For p = (1, 0) and x = (x₁,x2,...,xn) ER", define ||2|p:= - ². |P Show that n jyjx|py|q for x, y…

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Q: Find the sum of (arctan(n + 1) – arctan(n)) if exists. Lütfen birini seçin: a. b. 3 2 d. e.0 DOO

A: Given- ∑n=1∞arctann+1-arctann To Find- The sum of the above expression.

Q: Use Euler-Maclaurin's formula to prove that E n %3D

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Q: Express the limit lim (3 cos (2ra* ) + 4)A¤¡ over [6, 8] as an integral. 2 CoS n- 00 i=1 9. Provide…

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Q: If f(x,y,z)=In(x²y+sin?(x+y))+111x112y2z113, then at (1,1,1) is equal to əx²əyəz

A: We have to find derivative

Q: 1 And the radios of Co for the pover Serie for the Power Serie vergence 00 xh (2"+1) (n?+1)

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Q: The diagonals of square LMNP intersect at K . Given that LK=1, find KN . 1 K KN =

A: For the following given question  Given,  LMNP is a square  and LK=1 then,

Q: The Lucas numbers L; are defined as follows: (1) Lo = 2, L = 1; and %3D (2) L, = L,-1+ L-, for n E…

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Q: Let C be the shortest path that connects a to ni and I = ſ, (sinhz + 1)dz. Then |=-1-cosh n+ n(i-1)…

A: First option is correct.

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.