Use trigonometric substitutions to evaluate the definite integral 1 [5x²³√1-x² dx.

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A: Please see the below picture for detailed solution.

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A: According to the given graph Absolute minima is the minimum value of the function

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A: I am attaching image so that you understand each and every step.

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A: The formulas we use: △y=f(x+△x)-f(x) dy=f'(x)dx d(kxn)=knxn-1, k is a constant

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A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

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Q: x − 2 lim x-2 √√√√x - √2)

A: SOLUTION-

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Q: Function g: H

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Q: Q3/ Solve the following second-order differential equations: three) 1- y"-y-2y = e³x

A: Note:- These are multiple questions and accroding to company guideline we can do maximum 1 question…

Q: Calculate the derivative. (Use symbolic notation and fractions where needed.) d dx (-9x³ + 4x² - 7x)…

A: Topic - derivative of a function. we are given function:-9x3+4x2-7xand we know thatddxxn=nxn-1

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A: This question can be solved using the equationV=Vo(1-R)n   WhereV=value of the machine after n…

Q: y = (ex-e-x) (ex+e-x)

A: To find the derivative

Q: 4- x x-45-√√x² + 9, 2 lim X→4 lim 9 - x² 2

A: Solution 1. limx→4  4-x5-x2+9When we put limit we get 00 indeterminant form:limx→4…

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A: Topic = Algebra

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A: we will find the  required.

Q: B. Find the indicated limit if it exists (2x+1 if x <3 if 3 ≤x 1. lim f(x) if f(x) = {10-x

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Q: QUESTION 2 1 1 Express as a single logarithm:In([x+ 2]³) + — In(x) − − In([x² + 3x + 2]³²) - 3 2 2…

A: I am attaching image so that you understand each and every step.

Q: [2^³] [_^ (^^) ] = Y

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A: Profit=Revenue-Variable cost-Fixed cost

Q: 1 5-Prove that cos (tan-¹ x) = √7X²' 1+x² -∞0 < x < ∞

A: The proof of the given inverse trigonometry problem is as follow.

Q: QUESTION 3 State the domain of: f(x)=√3-1-√2+t O [-2,3] O (-∞, -2) U (-2,3) U (3, ∞ ) O [-3, 0⁰0) 0…

A: Domain:- All those input values of a function such that function at those values exists.

Q: x³ - 1 3 lim x-1 x - 4

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A: Formula: Domain of a square root function: f(x)= √y  can be find by y≥0

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Q: [ 2 3t+4 dt

A: Topic:- calculus and application of integration

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Q: Find the wait Vector of The Vector B as be shown in the Figure YF 181 - 10 unit B 37° xx

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Q: Evaluate the integral S 0 16- using trigonometric substitution.

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Q: Solve the following differential equation. 2y""+11y'''+18y"+4y'-8y=0

A: We have differential equating 2y4+11y'''+18y"+4y'-8y=0 Auxiliary equation 2m4+11m3+18m2+4m-8=0 Lets…

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A: Given Graph:-

Q: Suppose that f(x) = X 4x-8 Then, The domain of f is {x € Rx # Number} and ƒ-¹(x) =

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Q: 3. Let f(x) = (3x² + 1)2. Find f'(x) in 3 different ways by following the instructions below in…

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Q: Find the domain, range, intercepts, symmetries and asymptotes of the following function 1. y = x³

A: 1. y=x3 Since you have posted multiple question in this question which are not interlinked so i have…