prove that :: 2) (1+i) (1-1)² = 64

Q: -1 t² Vta 6 dt

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Q: fe e sin xdx

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Q: -2- 0 y = g(x) 4 7 x

A: To evaluate the integral.

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

A: Please see the below picture for detailed solution.

Q: 15. Show that the equation, 2³ + e* = 0 has exactly one real root.

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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: 9. TC/2 (3 sin² t cos ti+ 3 sint cos² tj + 2 sint cost k)dt

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Q: Q3/ Solve the following Second order differential equations. 2- d²y dx² +3+ 2y = e-x + e-2x -

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Q: Sketch the plane curve. r(t) = 3ti - tj, [0, 3] y O 2 1 -1 -2 y 3 2 - -1 -2 2 4 4 Find its length…

A: This question is related to vectors and parametric equations, we will solve it using given…

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: Q1/ Solve the following differential Equations. 1- (1+x2)dy-xy dx = 0

A: To solve the differential equation.

Q: Use the substitution u = 3x²-2 to find the following indefinite integral. Check your answer by…

A: We need to find integral.

Q: Q1: Fill in the blanks for the following statements (chose five only) 4n 1. lim→∞ 2n+1 log10 (3x -…

A: The objective of the question is fill the blanks.

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: dy Q5: Find for the following functions: dx (3) y = ex.sin² x In√x

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Q: Q2: Solve the following integrals: (1) 7x²+14x+15 (x²+3)(x+7) dx ; (2) sin6 x+cos6 x sin ³ x cos³ x…

A: According to our guidelines, we can answer only one question or three subparts of a question.other…

Q: 04: Answer two only: (A): I A-2 1 -1 1-2 Find AB and AC.. -- 3 1 1 and 1 3 1 CO

A: Given :A=420210-2-11, B2312-2-2-121, C=31-3026-121

Q: The radius of a right circular cone is increasing at the rate of 6cm/sec while  its altitude is…

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

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

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Q: Use polar coordinates to find the limit. [Hint: Let x = r cos(0) and y = r sin(0), and note that (x,…

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Q: 61. A "bead" is formed by removing a cylinder of radius r from the center of a sphere of radius R…

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Q: Suppose f(x)dx= 2 and f f(x) dx = 1, and f3f(x)dx=-6, what is B. 2 C. 3 D. 4 A.-2 f(x)dx?

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Q: An experiment was conducted to determine the effects of elapsed time on a person's memory. Subjects…

A: We have to find the average percent recall after 1 hour, the expression for the rate of change in…

Q: a. For the following function, find f'(a). b. Determine an equation of the line tangent to the graph…

A: To find f'(a) & equation of tangent:

Q: 7. f* (x² + 8) & dx CO (³ (x-1)

A: We have to solve integral

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

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Q: 38.Calculate the surface area of the surface obtained by revolving the curve y = √9-x² around the…

A: Note to student :    Thanks for posting your queries. But there are multiple questions given. As per…

Q: Sketch the function. v(x) = 0.2(x-3)²(x+2)³

A: We can answer the question as below.

Q: Find the solution to the initial value problem. dy = 2√√√√t, y(1) = 7 dt y(t) =

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Q: 9. (x²-x+y) dx - x dy = 0 10. (2y² + 2y + 4x²) dx + (2xy + x) dy = 0

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

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Q: Q3: Evaluate the following integrate: (chose three only) 1. dx 1+x4 2. ex-edx ex+e-x 3. fxsec² x dx…

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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: Find the indefinite integral. (Use c for the constant of integration.) (2ti + j + 9k) dt 2ti + tj +…

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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: 2. y = Arctan

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Q: (A): solve the following linear equations by Cramer's rule: x + y + 2z = 1 2x-y-z = 0 x +2y-z = 4

A: Calculation of determinant is the key requirement of this problem.

Q: Q5: Find dx for the following functions: (3) y = ex.sin² x In√x

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

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Q: 04: Answer two only: (A): IF A-2 10 1-2 -1 Find AB and AC. 3 and C-0

A: Given :A=420210-2-11B=2312-2-2-121C=31-3026-121

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: Evaluate the definite integral. S √4x + 3dx

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Q: a. For the following function, find f'(a). b. Determine an equation of the line tangent to the graph…

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

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Q: X y = x + Ae^ + Be - 2x

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Q: 013 Verify that the function satisfies the two hypotheses of Mean Value Theorem on the given…

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Q: Find the general isolation of the following: 1. (x³y³+1)dx +x4y²dy=0

A: Please see the below picture for detailed solution.

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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Q: Consider an exchange economy with 2 consumers, A and B, and 2 commodities, x and y. Each consumer is…

A: Multiple subparts are asked, I am answering first 3