Suppose that ƒ is a positive-valued function with lim supƒ(x) = L > 0. Prove x→a that lim inf=1- f(x) x→a

Q: 13. Find the length of the curve 1 8 4y² X = =+₂ from y = 1 to y = 4.

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A: Given that Sn=3x12∆x1+3x22∆x2+...+3xn2∆xn, where the ∆xi fill out the x-interval from x=-2 to x=6…

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A: t: ℝ3→ℝ3x,y,z↦2x,y+z,z-x

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A: This is a question of Relation.

Q: O List the first 5 elements of the sequence defined below. = 2 a1 = an = 2an-1-3, n ≥ 2

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Q: 5. Determine whether or not the expression is satisfiable. (x₁ V2 V3)^(x₁Vx2 VT3)^(T₁ VT2 VX3)

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Q: d) Determine whether Prove it, if not give Ris e) Determine whether If not Ris antisymmetric a…

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Q: An unbiased dice, with faces numbered 1, 2, 3, 4, 5, 6, thrown n times and the list of n numbers…

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Q: Jady has 24 coins, some nickels, some dimes, and some quarters. He has 4 more nickels than dimes,…

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Q: Evaluate the line integral Vp dr for the following function and oriented curve C (a) using a…

A: Evaluate of parametic line Integrals

Q: Find the Inverse Laplace transforms of the following functions:   (4s + 2)/(s2 +6s + 34) 1/…

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Q: Suppose A is a 2 x 2 matrix, where u= Au = Submit Question 2 5 30 -A~A 3 A³u- 13 A'u The minimal…

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Q: Evaluate the surface integral x² +2² Y where S is the surface represented by r(u, v) = (2 cos v, u,…

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Q: The gradient of the line 8y + 12x = 7   is

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Q: When money is shared in the ratio 2: 3: 5 The smallest ratio got  $80,000. How much is the largest…

A: answer is d $200, 000

Q: Find a power series representation for the function rsin(5) on (-00, 00). α 1. f(x) = Σ (-1)"-1 n=1…

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Q: The differential equation: d'a +b+cx=0 has a solution given by: y = e* (A sin 6x + B cos ßx) where a…

A: The given problem is to find the values of A and B for the given solution of the differential…

Q: -5<x<0 0≤x≤1, ther (11, 1<x<5 If f is the Fourier series of g(x)=9x, f(x) = 0+ ]) cos (152) + (sin…

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Q: Aakash has a liability of 6500 due in 6 years. This liability will be met with payments of A in 2…

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Q: Find a power series for the function, centered at c. 1 f(x) = C = 3 8-x f(x) = 00 Σ n=0 X Determine…

A: We have to find the power series of the given function.

Q: A tank contains 80 kg of salt and 2000 L of water. Pure water enters a tank at the rate 10 L/min.…

A: A tank contains 80 kg salt and 2000 L of water. Pure water enters a tank at the rate 10 L/min. The…

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Q: g) sec 20+sec 0 =0

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Q: 1.23. For a point of the curve of intersection of the surfaces (+): C x − y = c . y = r tinh show…

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Q: (a) State which of the following matrices are in row-reduced form: 1 0 4 -1 1 -1 0 - - ( ) --- ()…

A: This is a question of linear transformation.

Q: (c) Check whether or not: Q (2¹/³) = Q(4¹/3) Also obtain (Q (2¹/³): Q].

A: We first find [Q(2^(1/3)):Q]  Then using this prove that Q(2^(1/3))=Q(4^(1/3))

Q: 3. 4. 5. t2 sin 3t-3t cos 3t 2 sinh 6t-4t cosh 6t 1²e-2t sin 8t

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Q: If the diffusion equation k and initial condition ӘФ dt 2²0 dx²² subject to the boundary conditions…

A: Given: k∂ϕ∂t=∂2ϕ∂x2 , 0≤x≤1, k=1 and ϕ0, t=0=ϕ1, t=0 ,ϕx, 0=100 To find a solution to a given…

Q: where y . Prove that at the point of intersection of the surfaces (4) y __x² + y² = z², z = a tan` =…

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Q: Determine the flux of the vector field F(x, y, z) = (x, y, z) across the portion of the paraboloid z…

A: Given: F→x, y, z=x, y, z , z=3-x2-y2 , z=-1 To find the flux of the vector field.

Q: The continuous function g, consisting of two line segments and a parabola, is defined on the closed…

A: Disclaimer: Since you have posted a question with multiple sub-parts, we will solve first three sub…