- (³77) 5³ where s denotes the length of the edge of the cube. Find ß. V(s) =

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Q: 3 (a) Find general solutions of the given differential equations: (i) y'"-6y' +9y = 0, (ii) y" - 6y'…

A: Note:-  As per your request i have done both sub parts of part (a)

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Q: -3. For the function f(x) = -5x - 3, find the slope of the tangent line at x =

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Q: ex 1₁-0² (1 - e²x) a. 3 b. C. ex VI d. √1 G ex ex 3 2 5 ² ( + 2 1-e(2x) 2 5 dx e2x In 1-e2|+C e2 + C…

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Q: QUESTION 7 Evaluate the double integral. FS= 3xy 2 RX²+1 OA. 8 3 OB. 16ln (2) OC. 8ln (2) OD. 16 3…

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Q: Calculate (t) when k(t) = r(t) = (6t¯¹, 1, 6t)

A: r(t)=6t-1, 1, 6t Formula for  curvature κ(t)=r'(t)×r''(t)r'(t)3

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Q: 12. Given the vector equation [x, y]= [3,1]+[3,-5] find a) the parametric equations b) the symmetric…

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Q: Find dy dx dy if y dx = x³ + 8x + 6 x² - 5

A: Given: y=x3+8x+6x2-5

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Q: 6. Find the functions whose equations in factored form have a factor that is cubed. These functions…

A: see below the answer and explanation

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Q: I. Find dy/dx of the following: COS X √4-3x² 7. y In- 8. y In, 6. y = In(In x) 9. y + ln xy = 1

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Q: Evaluate the integral below by interpreting it in terms of areas in the figure. The areas of the…

A: answer is in next step. please give a like!!

Q: 9. Given vectors = [3,-6,8] and v= [4,-2,-5], determine uxv.

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Q: J dx 4+x²

A: Given,            ∫14+x2dx

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A: NOTE- "Since you have asked multiple question, we will solve the first question for you. If youwant…

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Q: Find the solution to satisfying _y(t) = dy dt = 2y y(6) = 9

A: The given differential equation is; dydt=2y As we know from the integral rule,  ∫1ax+bdx=1alnax+b+C

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Q: Find the extrelne values of the function f(x,y)=4x2+ 7y2, on the circle x² + y²=1.

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Q: 7-x, x4. Complete parts a through d below. Let f(x) = a. Find lim f(x) and lim f(x). Select the…

A: Given that a limit problem and we solve by  using limit method of right-hand  and lefthand  limit…

Q: 8. Use the Chain Rule to find az/as and az/at. z = (y-2x)³, x = s³t², y=s+t²

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Q: Consider the function f(x) = 4x + 4x7 4x³ 8. An antiderivative of f(x) is F(x) = Ax" + Bxm + Cx² +…

A: The given integral is fx=4x9+4x7-4x3-8 Integration formulas: ∫xndx=xn+1n+1+C∫dx=x+C

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Q: 1. Evaluate. a) lim x--2 ³-2x² +12 x² +1 x² -8x+7 b) lim x-7 2. What is the average rate of change…

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Q: 1. S(√t -√√² + √√³) dt

A: solution ) ∫ ( t - t2 3 +t35 ) dt = ∫ ( t1/2 - t2/3 + t3/5 ) dt  we know that  ∫xn = xn+1/n+1  = (…

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Q: 3 If f(x) = 2 + x, evaluate Σƒ (k+1). atas (k k=1

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Q: (a) √3x³ + 3x - 2 dx (b) √3x²+√x dx √x (c) főz (z ² − z− ¹) dz (d) 2² (3−u)(3u + 1) du

A: Since, you have posted multiple questions, as per guidelines we will solve only first question. If…

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A: The objective is to use interval notation to determine where f(x)&gt;0. 2 and use interval notation…