Solve the given differential equation 5x4cos 2 ydx - dy = 0 (A) y = tan-¹ (x5 + C) B) y=x5+ C C y = tan (x³ + C)

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Q: Q4. A. Evaluate: w = [2 + 2√31]50

A: Let's evaluate given complex number equation.

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A: Formulas used for tan: Tan2θ=2tan(θ)1-tan2(θ) Tan(θ)=1cot(θ)Tan(2θ)=sin(2θ)cos(2θ)

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A: The average rate of change at a point is given by, Rf'(x)=f(x+1)-f(x)x+1-xLf'(x)=f(x)-f(x-1)x-(x-1)

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Q: 1. Prove using index notation. ABC REF = AB (c@f) E¹: R ":"product is defined as where := Pij Qiz…

A: Given ......  A~B~c~ · D~E~f~ = A~B~(c~⊗f~)E~T:D~                 Where,…

Q: 1.) f(x)=(2x-5)(3x-4)

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Q: 3. Find the derivative of f(x) = cos¹ (3x²)

A: Solve 3

Q: Find a function that satisfies the given conditions and sketch its graph. 40) lim f(x) = 0, lim f(x)…

A: Solution: 40) limx→±∞f(x) =0 , limx→1-f(x)=∞, limx→1+f(x)=∞   Check each condition

Q: Find f + g, f-9, fg, and f/g and their domains. f(x)=√√16x², g(x) = √√x + 2 Find (f + g)(x). X Find…

A: Find the function and their domain

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A: Given surface area, A= πr2+πrl  Taking derivatives each sides we get, dA=2πrdr+πldr+πrdl...(i)

Q: 11.3 Q5&Q6 I need both questions ? percent correct answer Needed to be solved both as soon as…

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Q: For f(x)=5x-1 and g(x)=x+1/5 find the following function (fog)(7)

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Q: 2x 2-3+ x - 3 Example 9. Find lim 2x x-3-x-3 and lim

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Q: S dx 2 (1+x²)²

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Q: Evaluate the integral. 2 X Jo x² + 4x + 20 dx

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A: Topic- Application of derivatives we are given P(t)=4.5t2-15t+180 where P(t) represents median home…

Q: Solve the D.E. 1. (D²+1)y= 12 cos² (x). Solve using 2-ways. ANSWER: y = C₁ cos(x) + C₂ sin(x) + 6-2…

A: Differential equation

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Q: Given the piece-wise defined function: 8 x < 0 f(x) = { 16 x ≥ 0 f(0) = Calculate the following…

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Q: Determine 1) a₁ = -3, r=4 if each geometric series converges or dive 3) a₁ = 5.5, r=0.5 5) 81…

A: Solution

Q: Use properties of limits and algebraic methods to find the limit, if it exists. (If the limit is…

A: Topic-Limits We are given,f(x)=9-3xifx&lt;3x2-xifx≥3Limit exists at x=c if limx→c-f(x)=limx→c+f(x)if…

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A: To evaluate the integral

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Q: Use the graph of the function f(x) below to answer each question. Round all values to the nearest…

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Q: 2. 2²-25 lim 1-25 r²- Ar

A: limx→5x2-25x2-4x-5 We have to find the limit value.

Q: Find the particular solution to the given differential equation that satisfies the given conditions.…

A: The given differential equation is 3y''+5y'-12y=0. The auxillary equation is given by 3D2+5D-12=0.…

Q: Q3. For the following matrices find x, y, z, and w, then check your solution. (2x + 5y)] 5y)] 2 6…

A: Need to find out the value of x, y, z, w.

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A: Let's solve.

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Q: If x²y³ - 9x sin(y) = 14, find y' by implicit differentiation. y' =

A: We can find the answer as below.

Q: 1. Solve the inequality. Give the solution in set and interval notation, then graph it. 2(x - 5) ≥…

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

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Q: The price per barrel of crude oil in the period 1980-2013, in constant 2014 dollars, can be…

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Q: Evaluate: w = [2 + 2√31]50

A: Given: w=2+23 i50.