Solve the following linear systems of differential equations.

Q: Write a polynomial f(x) that satisfies the given conditions. 2 Polynomial of lowest degree with…

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Q: 0²1' (19²¹) = (1) 1

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Q: For what values of a and b is the line 2x + y = b tangent to the curve y = ax² when x = 4?

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Q: Solve the given initial-value problem. y(x) = y" + 6y' - 7y= 11e²x, y(0) = 1, y'(0) = 1 2x 7e -7.x +…

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

A: We can solve the answers as below by finding the derivatives.

Q: Question 2 Find a differential equation whose general solution is y = c₁est + c₂e-2t. 0 2

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Q: Determine whether the improper integral diverges or converges. 16 1 √√√x dx converges diverges…

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Q: Describe the domain and range of the function. f(x, y) = In(xy-1) Dor

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Q: Solve the initial value problem 25y" — 40y' + 16y = 0, y(0) = 2, y'(0) = 3. y(t): How does the…

A: We can solve this as follows:

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

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Q: 2: Solve the following integrals: - 7x² +14x+15 (x²+3)(x+7) dx ; 1) S

A: Given: ∫7x2+14x+15x2+3x+7dx

Q: 4. C(x-xxx

A: 4. ∫-342x5-3x4+4x3dx Note:    Multiple questions are given, we are answer only one question. If you…

Q: 4 (A): If A = 2 -2 Find AB and AC. 2 01 1 -1 0; 1 2 B = 2 -1 3 1 -2 -2 and 2 1 3 C = 0 1-31 6 1 2 -1…

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Q: Given: f(x) = 0.2 + 25x-200x^2 +675 x^3-900 x^4 + 400 x^5 from a = 0 to b = 0.8 and segment equal to…

A: Given that      f(x) = 0.2+25x-200x2+675x3-900x4+400x5   from a=0 to b=0.8 and segment equal to 8.…

Q: 7. Use integration tables to find or evaluate the integral. (Use C for the constant of integration.)…

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Q: 1.5 Integrate 10(2x + 1) dx Answer 1

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Q: xdx x²+6x+18 7. f cos(lnx)dx 8. fest sin(at) dt 6. f

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Q: (1) Find the Taylor series for f(x) centered at the given value of a. (Assume that f has a power…

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Q: Find the critical points of the given function. a) f(x) = 2/3+¹/3+x−2/3

A: Since multiple questions are asked, I am answering first question

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

A: Given a- cos (x+y) dx +(3y² +2y +cos (x + y) )dy =0 b-y'=(x+1)e-xy2

Q: Evaluate the integral by first modifying the form of the integrand and then making an appropriate…

A: We have to evaluate the integral by first modifying the form of the integrand ∫ [ln(e8x) + ln(e-8x)]…

Q: Describe the domain and range of the function. xy x-y z Domain: 0 {(x, y); y # 0} 0 {(x, y): x*y} O…

A: To find domain and range of the given function.

Q: Find the critical points of the given function. 1 a) f(x) = -√24/3+2¹/ +2-2/3

A: Since multiple questions are asked, I am answering first question

Q: Describe the domain and range of the function. F(x, y) = 5x² - y Domain: 0 {(x, y); x = 0} 0 ○ {(x,…

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Q: The line graph shows the average number of awakenings during the night for men and women of…

A: To find the difference between the average of awakening during the night.

Q: Find the radius of convergence, R, and the interval of convergence, I, of the following series. (1)…

A: (1) The given series is ∑n=1∞n(x-1)n

Q: Solve the initial value problem 25y" - 40y' + 16y = 0, y(0) = 2, y'(0) = 3. y(t) = = How does the…

A: We have to find the solution of given initial value problem.

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: (18) Find the derivative of the functio 2²+5 3 Y=2²-5 Nor me it to Vitou inst

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Q: 12 - y+ ] - dy = |+C

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Q: Find the general solution of the following differential equation. 64y" +80y + 25y = 0 NOTE: Use c₁…

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

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Q: Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = x 2…

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

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

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Q: 2. y = Arctan

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Q: (C): If w = tan x and x = 4²³ +t: Find?

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Q: Use the figure below to find the exact value of the trigonometric function of angle A. sin(A) 00 7 A

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Q: 3. (x³+xy²-y)dx + (y³+x²y+x)dy =0

A: We need to find the solution for (x3+xy2-y)dx+(y3+x2y+x)dy=0

Q: 2 -1 -x²+8x-4 dx 1 x(x²+x-2)

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

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Q: Compute the partial sums S2, S4, and S6 of 1 1 + 5.6 6.7 (Use symbolic notation and fractions where…

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Q: Find an equation of the plane tangent to the following surface at the given points. zexy; (1,0,1)…

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Q: Initial speed is not 98 ft/s. What is the initial speed

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Q: Given f" (x) = 8x − 6, ƒ' (1) = −3, and f(1) = 5 find f(x).

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Q: Discuss the continuity of the function. 41 √x² + y² + z² f(x, y, z) == continuous except where x² +…

A: The given function,   fx,y,z=41x2+y2+z2

Q: |-*^= 39. What is the length of the curve y = √x- between x = 0 and x = 2?

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Q: Suppose that f is integrable on [-4, 7]. If the average of f on the interval [-4, 7] is 4.25, fin 4…

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Q: Q3 :(A): By using "L' Hopital rules "; Find the limits of : (2) limx-o x-³ (tan-¹x - x)

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Q: 12. x² sin(x + y) = 1, -

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