2. Find the area of the region enclosed by the parabola y = 2 - x² and the line y = -X.

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A: This question is based on gradient of function at a point.

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A: Solution is given below:

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A: Last 2 question solved

Q: Find the curvature of the curve defined by the function y=3x^2 - 2x + 4 at the point x=2

A: Curvature is defined as : K(x) = |y"(x)| / {1 + [y'(x)]^2}^(3/2).  Note that :- |y"(x)| means the…

Q: Integrate (3-2)¹0 dar Select one: OA.(3-2)¹¹ +C OB.(3-2)¹¹ +C 12 OC.(3-2)¹¹+C OD.(3-2)¹¹ +C 10

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A: Since you have posted multiple questions. As per guidelines we"ll solve only first first question.…

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Q: Integrate 3+22 Select one: OA. 7Inlxl + OB. 4inlxl + O C. 31nlxl + O D. 5Inlxl + dz + C + C + C + C

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Q: 15 0 2) is an eigenvector of the matrix 25 -12 -6 A = 60 -31 -15 -36 22 10 associated with the…

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Q: Question 35 If z = x arctan 0 - 4 OFF O undefined ◄ Previous (²).find əz əx at x = 0, y = 1, z = 1.

A: To find the partial derivative of z with respect to x.

Q: The graph shows the ellipsoid x² + 4y² + z² = 16. Use the graph to determine the equation of the…

A: The given data is: x2+4y2+z2=16 Let  fx,y,z=x2+4y2+z2-16 Now, fx=2xfy=8yfz=2z

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Q: A polynomial f(x) and one or more of its zeros are given. f(x)=x²-2x³+3x²+4x-10 1-2i is a zero

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Q: Decide if Rolle's Theorem can be applied to f(x)=x² - 4x² + 4x² +1 on the interval [-1, 3]. If…

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Q: What is f(x) of f(x) = log3 (1-2x)²? -32 In(3)-(1-2x)³

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A: Since you have posted multipart questions. As per guidelines we"ll solve only first three parts.. If…

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A: The given differential equation,     yeydx=y3+2xeydy

Q: 4. Use the bisection method to approximate the root of f(x) = 2x² [0, 1]. Let € = 0.1 be the margin…

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Q: What is f (x) of f(x) = 320 (2x-7)³ O4x²-28x-31 (2x-7)¹ [(8x-28)-4(4x²-28x-31)] (2x-7)¹ O4x²-28x-31…

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Q: The limit: lim (x,y)-(0,0) exists, and equal to 0 Select one: O True O False x - y x² + y²

A: Here, we will try to evaluate the limit value of lim(x,y)→(0,0)x-yx2+y2

Q: Question 40 The graph of y=2 is concave downward for all values of such that. 0 x 2 0x 0 < Previous

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Q: Use Linear Approximation to estimate Af = f (7.01) - f(7) for f(x) = x². (Use decimal notation. Give…

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Q: 1. Evaluate Sox2+4* dx 2. Find the area bounded by y = 4x², x = 2 and x = 6. 3. Find the area…

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Q: Find the points of inflection of the graph of the function. (Round your answers to three decimal…

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Q: Sketch the region enclosed by y = 3x and Y = find the area of the region. 2x². Decide whether to…

A: Given that y=3x and y=2x2To find : Area between the region.Solution :

Q: A particle is moving with acceleration a(t)=30t+8a(t)=30t+8. its position at time t=0t=0 is…

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Q: Use Newton's method to find the absolute maximum value of the function f(x) = 5x cos(x),    0 ≤ x ≤…

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Q: Use the Integral Test to determine whether the following series converges after showing that the…

A: If f(x)  is a continuous, positive and decreasing function on the interval [k,∞)  and  f(n)=an…

Q: Find the directional derivative of the function at P in the direction of v. f(x, y) = x³y³, P(8, 3),…

A: Here we have to find the direction derivative.

Q: lim cot 1 -1 8418 1

A: A detailed solution is given below.

Q: Answer the following True or False. If 0 < a < b and 1 < c .be 1 then: c b 1 |--L -dx x True O False…

A: Given.

Q: Find the gradient of the function at the given point. Function Point (3, 7, 2) f(x, y, z)=√√√√x² +…

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Q: S dz zlnz (Inz)²-1 Select one: O A. Q B. O C. Q D. arcsec(Inx) + C arcsin(lnx) + C arccot(Inx) + C…

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Q: F. (DERIVATIVES OF EXPONENTIAL AND LOGARITHMIC FUNCTIONS) 1. Find f'(x) if f(x) = 3e². 2. Find g'(x)…

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Q: Work Problems ( your works 1) Let F(t)=(4t — t²)i+t² j+sin(5t — 10) k - - - You need to show all a)…

A: Given: Ft=4t-t2 i+t2 j+ sin5t-10 k

Q: Estimate Ay using differentials. .1/3 y = x¹/3 e³x-1, a = 1, dx = 0.1 -

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Q: 1. y (4x + y) dx -2(x²-y)dy = 0 2. (2xy4e + 2xy³ + y)dx + (x²y4ey - x²y²-3x)dy = 0

A: We have to find Solution for given D. E

Q: Find dy/dx by implicit differentiation and evaluate the derivative at the given point. dy dx At 4, x…

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Q: or the function f(x)=sin(x), write Newton's formula as xn+1=F(xn)=xn−[f(xn)f'(xn)] for solving…

A: The given function is f(x)=sin(x) We need to solve for, f(x)=0 using Newton's formula:…

Q: Choose all critical points of the function f whose gradient vector is Vf(x, y)= ○ (0, 2) O None of…

A: We have to choose correct option for all critical points.