3. f(x)=x-x³-x²+1 3

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Q: Use the Laws of Logarithms to expand the expression. In(x√7) In(x) + In + In (√²) N X 27

A: Given query is to expand the expression.

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A: Topic = Derivative

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A: topic- derivative of a function

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A: We need to evaluate integral.

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A: Note: As per our guidelines we are supposed to answer only one question if there are multiple…

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Q: के For the function f(t, x) = sin(4xt +9x), find and da Əf 4x6x(4xt+9α) (Type an exact answer in…

A: topic- partial differentiation

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Q: The divergence test applied to the series 4k (7k + 9)* tells us that the series converges.

A: Given: Here,              ak=4k(7k+9)3≈4k73k3=473k2=bk(say) Now,                 limk→∞ akbk=limk→∞…

Q: 1. f(t) = (t5+t) (t³ - 4t+1) 2. g(x) = (+1)(3x - 1) 3. h(x)=¹

A: Topic:- function

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Q: find the derivatives: 1. y= (tan x)/ (1 + tan x)

A: Solution: 1. y= (tan x)/ (1 + tan x) y'=ddxtan x1+tan x

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A: We should recognise the t and do the appropriate calculations.

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Q: Find the arc length of the curve given by r= sin 0, 0s0< E a) 27 b) T c) 72 e) None of these O a.) O…

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Q: 5. fx³√√4 - 2x² dx

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Q: 6. Find the area of the region bounded by the curves y = x + 1, y = 9-x², x=-1, x = 2.

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A: Here I am providing my handwritten solution

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A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

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Q: Solve the system of differential equations. x₁' = 3x1 - 1x₂ ¸x₂' = 1x₁ + 5x2 x₁ (0) = - 11, x₂(0) =…

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Q: lim ∞ + X 3x² + 2x - 1 3√7+4x+x² + 3x

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Q: (e) Sketch a graph of g(x).

A: We need to find horizontal asymptote and graph.