Solve the following differential equations. Show your complete and detailed solutions. dy xy-y + 2x-2 dx xy+2y-x-2 1. : y (-1) = -1

Q: Rewrite the vector equation r(t) = (−4 − 3t)i + (3 − 2t)j + (−1 − 5t)k as the corresponding…

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Q: If lim g(x) = 6and lim- X-4 A B C D 3 6 √√3 √f(x)-1_√2 g(x) √6 ,whatisthe limf (x)?

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Q: Find the first derivative of: i. (3x − 5)^-5

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Q: The differential equation y - 2y - 3x2=0 is linear and homogeneous. A FALSE B TRUE

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Q: DIFFERENTIAL CALCULUS UPVOTE WILL BE GIVEN. PLEASE WRITE THE COMPLETE SOLUTIONS LEGIBLY. NO LONG…

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Q: Which is equivalent to Inlyl=3x + Cwhen y is solved in terms of x ? (A y = 3x + C By=e³x+C (D) y =…

A: To find the equivalent equation for the given function.

Q: (i) Let F(x) be a power series. Then the radius of convergence of F(x) can be negative.

A: This is a problem related to power series. Please follow the procedure given below.

Q: Find the common difference and the 100th of the arithmetic sequence   If a5 = 6 and a14 = 42

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Q: What is the general solution of the differential equation y" - 2y +y=0? A B © (D) y=C₁₂e¹+C₁₂xet y=C…

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Q: 21. cos(sin-¹)

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Q: Forms used: y-y1=m(x-x1) M= y2-y1/x2-x1 Y=mx+b I was supposed to write an equation for these…

A: There is a little calculation mistake. The whole solution has been given here. Assuming the question…

Q: The table shown gives selected values of x for the function h. 6 6.001 6.01 6.1 7 h(x) -7010 -7001…

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Q: Find the general solution of the Differential Equations: 2)(x² − xy + y²)dx - xydy = 0

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Q: XP ₂2/x-³ J 72.

A: This is a problem related to integration. Please follow the procedure given below.

Q: Use the properties of natural logarithms to simplify the function. X f(x) = In (1/1) f(x) = + In 4

A: The function is given by fx = lnx4+ln4To evaluate: The simplified expression of the function using…

Q: 38. f(x) = = 1 3x - 2³ C=-1

A: We can solve it as follows for Taylor's series.

Q: Consider the graph of the function /(x) below. Which of the following is true? 1. lim f(x)…

A: NOTE: Refresh your page if you can't see any equations. . as we can see the left-hand side of the…

Q: Determine the value of ksuchthatf(x) = Blank 1 Add your answer 7x=2 kx² yxs ifx > 1…

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Q: 11. 2n+1 ΣΕΡ 201 n=1

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Q: State the order of the given ordinary differential equation. (sin 8)y" - (cos 0)y' = 9 Determine…

A: Given the ordinary differential equation is sin θy''' - cos θy' = 9

Q: Find d²y| dx² d'y dx² x=2 = , where y = = P 4x5 - 2x². 4

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Q: The differential equation 3 (3x² + y2) dx-2xydy=0 is homogeneous of what degree? A) 4 3 (C) 1 2

A: The explanation of answer as follows

Q: The following function expresses an income tax that is 20% for incomes below $5000, and otherwise is…

A: To find out the taxes

Q: Find the derivative of the function. y = In(x√x² - 9)

A: To find out the derivative.

Q: Let lim g(x) = L. Which of the following is necessarily true? A (В D g(x) is continuous at x = a…

A: Given: The given limit is limx→agx=L To find: we need to find the necessarily true statement about…

Q: PROBLEM 3 [COMPOSITE AND INVERSE FUNCTIONS]: Two functions p(x) and q (x) are inverses of each other…

A: Given: The given functions are p(x)=3x-24x+5, q(x)=2+5x3-4x To prove: we have to prove that the…

Q: The second column of the matrix of change basis from the basis B = {u= (1,1,1); v = (1,0,1); w=…

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Q: 28. y = (csch-13x)4

A: y = (csch-13x)4 derivate this here we have use chain rule and do derivate . calculation is given in…

Q: Which of the following is the appropriate substitution for the Bernoulli differential equation xy' -…

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Q: Q4/ Find the maximum and minimum values of the function F = x². constraint 2x + y-z-5=0. Q5/A-…

A: Since, you have posted multiple questions, as per guidelines, we"ll solve only first three…

Q: 4) Find the following by using the substitution z = tan cos e de ii) sine cose + sin € dx ii) 1+ sin…

A: As per the guidelines I am supposed to do the first question among multiple questions, so here I am…

Q: What is the general solution of the differential equation 2y"'+y' 6y=0? Ⓒy=C₁e ² + + C₂ e ² A B…

A: We have to find general solution of differential equation.

Q: 2. Compute (16−1/16)4.

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Q: After t weeks of practice, a typing student can type 100(1e-0.5t) words per minute (wpm). How soon…

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Q: Find an equation for the tangent line of the curve 2(x2+y2)2 = 25(x2-y2) at the point (3,1) by…

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Q: Q / If you have th matrices S and M be the determinant of [₁ L60 55 48 M= 10] 14 43 10 /M*S/= S

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Q: - 2 to The region bounded by the line 2x + 3y = 6 and the x and y axes is rotated around the line y…

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Q: Let limf(x)=L(Lbeanyrealnumber) andnbe apositive integer. X→C Whichof the givenstatementsis/are…

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Q: Parametrize the intersection of the surfaces x² + y² = z², 7y = z² using t = z as parameter. (Use…

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Q: Find the exact arc length of the curve over the interval. y = 3x³/2 from x = 0 to x = 1.

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Q: Find the length (in units) of the curve  y =  16 − x2  between  x = 0  and  x = 2.    units

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Q: If x = √x^5y^5 + x^2y + xy^2, find:   zy zxy

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Q: (j) Let f(x) be an infinitely differentiable function. Let F(x) be the Maclaurin series of f(x). If…

A: The general notation of Maclaurin series is given by  F(x)=∑n=0∞fn0n!xn

Q: Which of the following differential equations is NOT LINEAR A There is no correct answer from among…

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Q: Determine the value of ksuchthatf (x)= kx2 ifx ≤ 2 2x+k ifx>2 iscontinuouseverywhere.Then, kerk

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Q: (4) Calculate the average value of f(t) (a) the interval [0, π]. (b) on the interval [0, x]. (c)…

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Q: Q4) Find the volume of the solid generated by revolving region bounded by curve y=√x and the line…

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Q: 48. iMa 2 n + 4n 3n4 +9

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Q: For the pair of functions f(x) and g(x), find the following. f(x) g(x) = x² + 1 f(g(x)) .) g(f(x))…

A: f(x)=7x and g(x)=x4+1

Q: Let f:(0,2)→ be defined by, f(x) = { 2x-1, (a) f is differentiable exactly at two points (b) f is…

A: To find- Let f : 0, 2 → ℝ be defined as fx = x2if x is rational2x - 1if x is irrational Then, f is…