Find all critical points of the function y = e(3 e² (3 – x²). Then, using the second derivative test, identify them as either minimum or maximum points, or neither. Of course, please show all of your work.

Q: a. On a rectangular cartesian coordinate system, sketch the parallelepiped having the vertices (1,…

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Q: Find the moment with respect to the y-axis of the area bounded by the parabola x = 4y - y² and y =…

A: Let's find moment with respect to you axis.

Q: A rectangular field having an area of 2500m² is to be enclosed by a fence, and two additional fence…

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Q: Find the volume generated by revolving the area bounded by x² + 4x + 4y + 8 = 0 and y=-2 about the…

A: We have to find the volume.

Q: INALTIIX Large Drop-Fro... Summary - Qui... George Floyd: '... Paraphrasing T... when did geor...…

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Q: For the following exercises, find aj dt and direct substitution. 225. f(x, y) = ln(x + y), x=e¹, y =…

A: Given;  f(x,y)=ln(x+y), x=et, y=et.

Q: Solve the first order linear ordinary differential equation x sin x dy dx + (sin x + x cos x) y =…

A: Here, the given DE can be written as: xsin xdydx+(sin x+x cos x)y=xex⇒dydx+sin x+x cos xxsin…

Q: 9 Determine the area to the right of g (y) = y² +4y-5 and to the left of the y-axis.

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Q: 16. Evaluate the integral or show that it is divergent dx x+1 1 (a) √ (3x+1)³², I (3+1), (b) /…

A: We need to find out here  integrals.

Q: 2π 3 [³* sin(y) + sec² (y) dy

A: We have to evaluate the given integral.

Q: Ju Solve the following equations by finding - suitable integerating factor. 11 v²dm + n(n+V) du =o

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Q: 6. Determine the Cartesian (scalar) equation of the plane that... a) contains the points (6,1,0) and…

A: SOLUTION-

Q: 5. Find the derivatives (a-b) and the limit (c): (2) ± √( 1 cos (1²) dt) (0) ² (154) dt dx 1 r2+x…

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Q: f(x) = 2x³9x² + 12x − 3 -

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Q: Compute[x² sin(2x)dx. A.- x² cos(2x)+ xsin(2x)+ cos(2x)+C 1 1 B. — — x² cos(2x)+ —…

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Q: 27 3. Explain how you would find the general term of the sequence: 4, -6, 9, - ".

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Q: Evaluate ſxy dx+(x+y)dy along the curve y=x² from (−1,1) to (2,4).

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Q: Set up, but do not evaluate, the integral to find the area of the surface generated when the curve y…

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Q: ƒ(x)=3x² +6x−9

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Q: x² - 25 to fill in the table: Xx - 5 6 5.5 5.1 5.01 Based on ONLY the table of values above, what…

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Q: -x+1 3+z Given the points R (1, -1, -3), the vector v = and the line d: = 1 + y = 3 2 1. Determine…

A: Both questions are solved.

Q: In an autocatalytic chemical reaction, the product form is a catalyst for the reaction. If Qo is the…

A: SOLUTION-

Q: -5x² +11x+2 x(x+1)² dx 2ln|x| +3 In|x +1| + + + C x+1 Option 1 2ln|x| +3 In|x +1| +++ C Option 3…

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Q: Find a set of parametric equations for the curve of intersection of the paraboloid z² +4y² -z = 0…

A: Here, to find the parametric equation of the paraboloid x2+4y2-z=0 and the plane 2x-z=0

Q: 6. If y = 3√x, then what is y'? A. y' = C. y' = ¹ x 3 x3 B. y' = 1/2 D. y' = ¹/2/2 x3 x 3 7. Which…

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Q: Evaluate the following integrals. -1 L₁ (3²- (3x² - 4x−¹+2) dx

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Q: Use Euler's method to solve the following ODES wwwwwwww dy dx = -2y + 4e¯*, with h = 0.18 from x = 0…

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Q: Question 4 Solve y at x = pi/3. cotx dy/dx = 1 - 2y, y(pi/4) = 1 0.75

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Q: 4 The slope of the tangent line to the curve y = X at the point 5, is: 5

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Q: 5. Suppose f is continuous on [2, 8]. Use the table of values of f to f(x) dx using a left, right,…

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Q: 4. Determine the number of terms in the sequence: -45, -32, -19, -6, 410 ***

A: There are 36 terms  in the sequence.

Q: he variable in each equation using a method of your choice. 93x+4 = 27-x+6

A: Given problem:- The variable in each equation using a method of your choice.   93x+4 = 27-x+6

Q: The curve defined by R(g) = 1. Considering f(g) to be a function such that f (1) = 0 and f' (1) =3.…

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Q: Determine the value of x when the slope is its maximum for the function f(x)=2cos(3x)

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Q: Solve the following trigonometric equation for 0 ≤ 0 < 2π. Show your work. 4 cos²x 3 =

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Q: f(x) = x² + 5x - 1

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Q: z = xey + y ex

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: 2. a+b+c=c+b+a is true because of

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Q: Find the volume generated by revolving the area bounded by x² + 4x + 4y + 8 = 0 and y=-2 about the…

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Q: rve (y+1)2 = 4x3 from x=0 to x=1? (4) =q8

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Q: S² z²√√(-z² + 1)5 dz

A: To find the value of the given integral.

Q: T/6 3 coss 3x dx

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Q: e formula C = (F-32), where F2-459.67, expresses the Celsius temperature C as a function of the…

A: Topic:- function

Q: Evaluation. 1. Determine the antiderivative for each. Show complete solution. √ 5x³=3 dx 2. √(√x√x +…

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Q: Find the area bounded by the parabolas (x − 3)² - 16ky = 0 and y² - 16k (x-3) = 0.

A: We have to find the area.

Q: Find the area bounded by the parabolas (x - 1)² = 4ay and y² + 4a = 4ax.

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Q: 18

A: We will solve the problem

Q: z²√(-z² + 1)5 dz

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Q: Ex: If w cos(uv), u = = xyz, y = π 4(x²+y²)' aw find at point (1, 1, 1). əx

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Q: Find the derivative of f (w) = 7ln (w) + 18.

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