Find the particular solution of the differential equation given that, when x = 0, y =-4 and Q3 * A.y=e^x (9x-4)-2sin(x) B.y=e^x (9x-4)-sin(x) C. y=e^x (3x-2)-sin(x) D.y=e^x (3x-4)-2sin(x) ele ele 11 dr -2ty= 3. +y=4cosx,

Q: Determine the slant asymptote of the rational function f(x) - Oy=5x-9 Oy = 5x + 9 Oy=5x-1 Oy= 5x + 1…

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Q: Q5: Find dy dx (1) In(x - y) = xy + y³; for the following functions: (2) y = tan³√/cot(7x);

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Q: Solve the initial value problem y" + 4y + 4y = 0, y(-1) = 5, y'(−1) = 6. y(t) = =

A: The given initial value problem is y''+4y'+4y=0,  y(-1)=5, y'(-1)=6

Q: Find f'(x) for f(x) = - 8A√x - 5Bx⁹ where A and B are constants. Completely simplify any fractions.…

A: Solution of given question is written in below steps.

Q: (C): It w = tan x and x = 4t³¹ +t: Find d?

A: Given that w=tanx  and x=4t3+t. We have to find dwdt. We can write,  dwdt= dwdxdxdt  [ using chain…

Q: Use the limit definition of partial derivatives to find fx(x, y) and fy(x, y). f(x, y) = x2 − 4xy +…

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Q: Q1: Answer two only (A): Solve the following linear equations by Cramer's rule: x+y+2z=1 2x-y-z=0 x…

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Q: F = (x²yz, - xy²z, -2xyz²)

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Q: Q5: Find for the following functions: dy dx (1) In(x - y) = xy + y³ ; (2) y = tan³√/cot(7x);

A: To find derivative.

Q: Q2: Solve the following integrals: (3) √ √dx dx (4) fxe* dx

A: The objective of the question is evaluate the indefinite integrals.

Q: of x³ (4+x²)² dx ; Use rationalizing substitution

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Q: The position vector r describes the path of an object moving in space. Find the velocity v(t), speed…

A: To find v(t) ,s(t) and a(t) for the given position vector r(t).

Q: (C): Solve the following equations:- (1) sin 2x + 2 sin² = 1

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Q: Set-up and evaluate the triple integral for the mass of the box 1≤x≤2, 1≤y≤16, 0≤z≤ with √√y density…

A: To setup and evaluate the triple integral for mass of the box.

Q: Find f if f"(x) = 2 + cos(x), f(0) = -1, f(π/2) = 2. f(x) =

A: Find f if f"(x)= 2+cos(x), f(0)= -1 , f(π/2)= 2

Q: 1) - 7x²+14x+15 (x²+3)(x+7) dx

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Q: doesn't this mean there are no critical points

A: Given the function fx,y=10x2-5y2

Q: Find all critical points of the following function. f(x,y) = 10x²-5y²

A: Please see the below picture for detailed solution.

Q: Q3 :(A): By using "L' Hopital rules "; Find the limits of : (1) limx-ol 1-cos x sin²x (2) lim, o…

A: 3 1) limx-0[1/(1-cosx) -2/sin2x ] 2) limx-0 (tan-1x-x) x-3

Q: f(a+h)-f(a) h a. Use the definition mtan = lim h→0 b. Determine an equation of the tangent line at…

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Q: Q1: Answer two only (A): Solve the following linear equations by Cramer's rule: x+y+2z=1 2x-y-z=0 x…

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Q: (B): Find the tangent equation to the curve y = sin² x at point x = T-3 π .

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Q: 10. dy dx = X y²√1 + x

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Q: f(t) = 4e-3t - sin 4t + cos 2t

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Q: The football game was attended by 237 people, down 40% from last week. How many people attended last…

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Q: 13. 2ny(8- y³/2) dy A) 4² (14 — y³/²) + C 7 2my 7 (14-y3/2) + C C) B) T² (14+y³/2) + C 7 D) 4²…

A: 13. The given integration is: ∫2πy8-y32dy To evaluate the given integral.

Q: 1 2 Identify the true statements. Incorrect 3 4 56 f(1) is a local maximum. f(5) is a local maximum.…

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Q: S 2 (2 x ² + 1 ) 1²/1 2 dx

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Q: Use the method discussed under "Equations with Linear Coefficients" to solve Problems 29-32. 30. 29.…

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Q: 3): Find the tangent equation to the curve y = sin² x at point x =

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Q: The after price tax on your new shiny car is $25,989.60. If a 4% sales tax was charged what was the…

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Q: Find the general solution of the differential equation y" 10y' +61y = 0. NOTE: Use c₁ and ca as…

A: find the general solution of differential equation y"-10y'+61y=0

Q: (B): Find the unit vector 3i - 4j + 5k perpendicular to the vectors: 4i + 5j-6k

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Q: Solve the following differential equations: a- (2x + 3y -2) dx + (3x -4 y +1) dy=0 b- (x²+3y²)…

A: The given differential equations are;  1) (2x+3y-2)dx+(3x-4y+1)dy=0 2) (x2+3y2)dx-2xydy=0.

Q: (B): Find the tangent equation to the curve y = sin² x at point x =

A: I have stated the used formulas in the solution.

Q: ddw? dt (C): If w = tan x and x = 4t³ + t ; Find

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Q: 2 Find the average rate of change of the function f(x) = x² + 7x from x₁ = 4 to x₂ = 5. The average…

A: Use average rate formula

Q: Use the method of reduction of order to find a second solution of the differential equation t²y" —…

A: The differential equation is given by,  t2 y'' - 4t y' + 6y = 0  Given,    y1 (t) = t2

Q: Q5: Find for the following functions: (4) y = x sinh 2x cosh 2x (3) y = e* sin² x In√x

A: The given functions,3) y=exsin2xlnx4) y=xsinh2x-12cosh2x

Q: Q2: Solve the following integrals: (3) √ √dx dx (4) fxe* dx

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Q: · 1. -1 (3-2x) ³ dx

A: The objective is to evaluate the integration.

Q: Compute u v if u and v are unit vectors and the angle between them is R|4

A: we know that u.v =uvcosθfor unit vector u=v=1given θ=π4

Q: For the vectors u = (6, 3, 4√5) and v= (3, 0, 5√5), evaluate the following expressions. a. 3u + 2v…

A: See this solution in below

Q: (B): Find the tangent equation to the curve y = sin² x at point x = 7.

A: I have stated the used formulas in the solution

Q: dw (C): If w = tan x and x = 4t³ + t; Find dt

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Q: (B): If A = 2i + 3j - 4k; B = 3i-4j+ 5k and C = i + j - k, find: (iv) (3A + 4B). C (1) A.B (ii) B.C…

A: The objective of the question is determine the addition and dot product of given vectors.

Q: The Doyle Log Rule is one of several methods used to determine the lumber yield of a log (in…

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Q: The marginal cost for printing a paperback book at a small publishing company is c(p) = $0.012 per…

A: Given data÷ Marginal cost  cp=$0.012 per page  Where p=number of pages

Q: (1) In(x - y) = xy + y³ ;

A: According to rules, I need to solve first question.. Please repost remaining questions

Q: 9. f dx 3x²√√25-x² 10. √ √² + 2tdt 11. f 3x+1 -dx 3x³-2x²-4 12. x²(x-1)(x+2) dx

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