Use the Taylor's theorem to show that a) fex+h) = fex)+h f

Q: use the inter medicte Value theorem to prove that 2 the equetion V2x+s -4 + x´= 0 has a root in…

A: intermediate value theorem: if the function  is continuous on and if  and  then the function has a…

Q: Let Li be the straight line segment from (0.0,1) to (1,a, 8) and let F: (z+ax, ay, x> Calculate the…

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Q: The contour of integral zdz of the cirle |z-i| =2 is

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Q: Prove that cosh-z = In (z + vz? - 1) %3D

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Q: If f=f(x, y), derive a forward finite difference approximation of 3rd order accuracy, O(h³), for…

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Q: Verify the Green's Theorem to evaluate the line integral . (2y²dx + 3xdy),

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Q: Use the trapezoidal rule with n = 5to estimate V7 + y³dy

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Q: /Evaluate The are bounded by The Semiellipes y =2J5-x' oP The line 6 X = ±1 ,Y=-1 %3D

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Q: Find the linear approximation of the tunction fox) = NT-x at a-0 %3D and use it to approximate the…

A: We find f'(x) using the power rule.   then we find f(0) and f'(0)

Q: Determine the area that lies under f (x,y) = 9x² + 4xy + 4 and above the rectangle given by [-1,1] ×…

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

Q: Define stpes to obtain the general solution of a 2nd order homogeneous ODE with real coincident…

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Q: Use the definition. that sinz •prove Z = UJZ %3D

A: Using definition of derivatives.

Q: he area bounded by the curve y = 3Vz and the lines z = 5 and z = 9 above the r – aris is_ quare…

A: Find the area of bounded curve with line x=5 and x= 9 above x-axis

Q: 3)Evaluate /y² + 1dA , Ris bounded by x = 4 - y² ,x = 0 R

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Q: 4. If R is the total resistance of three resistors, connected in parallel, with resistances R, R,,…

A: as per our guidelines we are supposed to answer only one question. Kindly re post other question as…

Q: Calculate the trapezoid approximation of o xdx using four subintervals. O T5 = 21.52 O T5 - 23.25 T5…

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Q: a) Evaluate the line integral TM UTM in terms of 7 where F = cos yi+ rj + ye*k and C is the line F…

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Q: Find the anc length oF t1x)=x° on [o,] Hint; use the Integral Tables,

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Q: Let T, be the approximation using n subintervals for the Trapezoidal rule to estimate I = +e*)dr.…

A: Error bounds for the Trapezoidal rule: Let f(x) is continuous function over [a, b], having the…

Q: If foxJ= S** t'dt, use the fundemental theorem of culcolus, part 1, to find f'cx) fixs=

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Q: Evaluate the integral Sdx using the two-point Gaussian quadrature rule 1+z² -2 2444 O O OOO N|WO…

A: We have to evaluate the integral ∫−2221+x2dx using the two-point Gaussian quadrature rule. Here,…

Q: Find the local linear approximation of f(x) = In(5 + x) at xo = -4. %3D In(5 + x)

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Q: Solve using horizantal Slide EX Evaluat..f.x.dA.whak.R.a.the.sgen.in.the figt.…

A: ∫∫R f(x,y) dA= ∫∫R f(x,y) dxdy =∫∫R f(x,y) dydx

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A: Multiplying and dividing first term by secx and second term by tanx of left hand side of equation ,…

Q: Find over xlapping area two equatione also gemetrical nepresentahon 2. 4'+v?=n, u?+cV- vn)=1 whore n…

A: Given curves are,…

Q: Suppose that f and g are integrable and that -1 f(x) dx = 5 h(x) dx = 4 7, dx = %3D Use the rules to…

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Q: b) Given UTMUTM VI+ approximate the integral using trapezoidal rule with h = 0.25. dr, UTMUTM

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Q: If f: [a, b] - R is bounded and has only a finit number of discontinuous points, then f is Riemann…

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Q: For the qutegradsSEddy tringle Over the bounded by -0,4=0 and *+y=l-

A: We have to find the integral  ∬e2x+3y dx dy   over the region R bounded by curves: x=0, y=0, x+y=1

Q: ae e drea under the curvé y=*from2-2to2 using a Rightt Endpoint approximation with 6 subdivisions..

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Q: evaluate the arca of He reginn bounded below by and y= aboue by y=X

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Q: Compute algebraically the resultant of the following complanar displacements: 100 N at 30°, 141.4 N…

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Q: Q5. Usung Maclaurin's thcorem expand, 5tanx as þar as +he term containing x". QC. Prove that , sinx…

A: A Maclaurin series is given by f(x) = ∑k=0∞fk(0)k !xk Given function f(x) = x5 tan x     Here, each…

Q: Evaluate So y? exy dA, where D 'is bounded by you, yit, x

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Q: bot A de groutne conitant. est Cheafuntis uh that f cark3 and f'4)=-s. g(xl=In (f(x)) + A conx)

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Q: consider the curue desoribed by 2y"-x²_4y vevity that the foint (4-25 les on this o8 wrE andd find…

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Q: 3. Evaluate JIJ 62² dV where G is bounded by x + 2y + 4z = 8 in the first octant.

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Q: /Evaluate The are bounded by The Semiellipes y=25-x' oP The lines X = ±1,Y=-1

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Q: J uore program Use a soft groping of ality aith motrix copobilities to'find the eligenualves the…

A: For any matrix, A , the eigen values are calculated by solving the equation, det(A-λI)=0 . Here , I…

Q: let X = * = zrs, find 22u in term f partial deriva bives

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Q: Ex: © Suppise that the fuowing trausfruntiun Cowneciğa the (I') and (xi) coarduate رک سهاور؟ てス4ス)…

A: Given  x¯1=ex1+x2x¯2=ex1-x2 Required Jacobian is…

Q: Suppose that f and h are integrable and that: i fx) = -1, f(x) dx = 5, h (x) dx = 4 ,Find: a. S–2…

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Q: 6 Use ik puer ris 1. 1+X to determine a at o, for FW)-n() poer res Centered the Funchon FW) - I…

A: We have to find the power series representation and radius of convergence.

Q: Evaluate the line integral ∫Cx^3z ds, where C is the line segment from (0,3,8) to (8,4,6).

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Q: Let S be the sphere of radius 2, oriented inward. Let F = (2x + e", 4y + e*, 2:2). Use the…

A: In the given question we have to solve the double integral s.t∫∫F.ds  to the help of divergence…

Q: find the volue of the od specify ingrol integrol T-x2 the

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Q: Given that F) = (yet coso)+(ayé-xsing)5 is conservative on R? (a) Find Potential gGay) Por F. (b)…

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Q: use the funda men tal Theorem of Culculus to find the under Curue of 2. y = -xFl0 x between x = 3…

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Q: Expand the function f(x) = tan x up to the first two non-zero terms in the Taylor's polyno- xn+1…

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Q: Prave by indretion ŽKczkt) z on n that for all integens aoenzl, 2.

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