J. nA(D) < // f(x, y) dA < M A(D) D is estimate to find an upper bound f (2 – y)/4 ITX 4 (쓸) dx dy. sin 0.

Q: Show that for some number a > 1, we have 1- <= In(a) <= a – 1. Hint: In(a) = S"dx, please check the…

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Q: 4.5 Estimate |7 - a dz using 5 divisions and Loft =O00000)-0 Right =O(00000)=C Midpoint = OO000)=0…

A: To estimate  ∫-7-4.5|7-x| dx using 5 divisions and left, right, midpoint, Trapezoid, and Simpson's…

Q: a) Find f'(x) where f(x) = xsin(a) +(sin(x))". b) Find all points on the graph of y³ –27y = x² –90…

A: As per Bartleby guideline, for more than one question asked only first is to be answered. Please…

Q: as indicated: f) t²x" + 3tx' - 8x = 0, x(1) = 0, x'(1) = 2. g) t²x" + tx' = 0, x(1) = 0, x'(1) = 2.…

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Q: 23. The graph of a differentiable function ƒ is shown. If h(x) = f(t) dt, which of the following is…

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Q: dy Prove that dx of x2 +2x is f'(x)=2x + 2

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Q: 8.. If L' { f(p)} = F (t) then L1 {f( ap) } is : a) aF(at) b) F (t/a) c) F(at) d) (1/a)F (t/a)

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Q: Si f"(t) = f (t) e² = e4t + 2t¹/4, ƒ'(0) = 2 et ƒ(0) = 3, alors =

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Q: / Fnd dy An CInsx) (4) (tan (2n 9x) secx e Y= (cot 5x)

A: Derivative using log

Q: The derivative of f(t) = 21° · h(t), where fand h are differentiable functions is: A. 10° · h(t) +…

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Q: O Find the derivative of the g f X COsy = ya sinx followny %3D 4) (2x+3y)"= e" tany %3D () sin xty)…

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Q: f(x)=\arctan (1-x),[0,1]

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Q: 7 (x³ + xy²) = 2y³ dy dy 8 (x2 – 1) +2xy = x %3D dx

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Q: xy + e^y = ln(x + y) defines y as a function of x implicitly for the most part. Express dy/dx in…

A: Given an equation, Where y is a function of x.

Q: 3. Find the *_ 2° L_weak derivative her XE [0,2TC] XE

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Q: Q3: Let f(y) = Ly]. Find a) f'({0}). b) f'({-1, 0, 1}). c) f'({y | 0 <y< 1}).

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Q: S (1/(X(Im)*) dx X(Inx)

A: LetI=∫1xlnx2dxLet u=ln(x)differentiate 1xdx=duI=∫1xlnx2dx.I=∫1u2du.I=∫u-2duUse power…

Q: Consider f(x) = xsin(x), find f'(π/2). (a) 0.03 (b) 0  (c) 1 (d) 1.5

A: It is given that, f(x) = x sin x we need to find f'(π2).

Q: Let f(x) = 3x° In f'(x) || f'(e*) =

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Q: t1 S[D] = [*ª dt D(t). By expressing D in terms of x and x = dx/dt, show that S[D] may be written…

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Q: Find the exact bound of the error in estimating using (a) Trapezoidal Rule, (b) Midpoint Rule and…

A: The given integral is  ∫14e3xdx We have to find error by using (a) Trapezoidal Rule, (b) Midpoint…

Q: 6. If f(w) = arctan w + 4", find f'(w).

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Q: Let f(x)= $ (x- 3)* k- 4k+1 8. Find: %| k=0 a) f'(x)= b) [ƒ(x)dx=

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Q: 4. Use Laplace transforms to solve the following initial value problems. (a) y"+2y-3y = 10 sinh 2t,…

A: Laplace transform.