Examine function f(x, y) = x² – 3xy - y²for relative extrema and saddle points.

Q: 3. S sinxdx 7+ cos²x

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Q: Find all solutions y' = (xy)^(1/3) y'= 1+x-y-xy.

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Q: Sketch a continuous curve for which each of the following statements is true. f(-1)=0, f(0) = 2,…

A: According to question,Given conditions,f-1 = 0,f0 = 2,f1 = 4,f'-1 = f'1 = 0,f'x <0 for the…

Q: The path r(t) = (t) i + (3²-2) j describes motion on the parabola y = 3x² -2. Find the particle's…

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Q: Suppose f(x) is continuous on [3,6] and-2 <f'(x) < 4 for all x in (3,6). L

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Q: 1. lim 1-2x - 3x² 1+x X→-1 2. lim X-2 3. lim √5+y-√5 y-0 y

A: Given: limx→-11-2x-3x21+x First, simplify the expression -3x2+2x-11+x: Factor the numerator:…

Q: Here again, is the triangle from Question 1. 4√3 X 30⁰ Enter the value of y here. If necessary,…

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Q: (x(t) Find a plane containing the point (2,-4,-2) and the line y(t) z(t) = = = 2 - 5t 4 - 3t 5- 4t

A: Equation of the plane general form is  a(x-x_1)+b(y-y_1)+c(z-z_1)=0

Q: Use the Limit Comparison Test for 4n² + 2 n(n-1)(n-19) Σ' an bn n=25 to prove convergence or…

A: The given series: ∑n=25∞an=∑n=25∞4n2+2nn-1n-19We need to prove the convergence or divergence using…

Q: Find the local linear approximation of f(a) = 2√ at x = 4. Oy=(x-4) O y-2√x-4 Oy=4 Oy=x+2

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Q: Find the average value of f(x) = = √x² − 1,1 ≤ x ≤ 6. - X

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Q: O O O O Which of the following shows an inconsistent system of equations? 3x + 4y = 5; 6x + 8y = 10…

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Q: Find the area enclosed by the ellipse a² b + y=-b√√√a²-x² y² 62 b y=1/√√a²-x² = 1 shown in the…

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Q: Sketch the curve given by the pair of parametric equations. x = t, y O A C B D Submit Answer A) B)…

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Q: √x f(x) = {3-x b) lim f(x) = Evaluate the following limits without graphing the function. a) lim…

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Q: What is the approximate volume of the solid created when the region under the curve y = cos z on the…

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Q: The base of a three-dimensional figure is bound by the semi-circle y = the x-axis are rectangles…

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Q: Factor -3x²+36xy – 60y² : = (x+ Hint: If the leading term is negative the gcf is negative. y) (x+ y)

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Q: S sinxdx 7+ cos²x

A: integration ∫sinx7+cos2xdx

Q: 1-16 Evaluate the line integral, where C is the given curve. 1. fcyds, C: x= t², y = 2t, 0≤ t ≤3

A: To evaluate the following line integral. ∫C y ds, C: x=t2, y=2t, 0≤t≤3 Note: Since, the student has…

Q: Given the ellipse: (x − 3)² 36 Find the center point: List the four vertices: + (y - 4)² 25 = 1

A: Given the ellipse: x-3236+y-4225=1 To find the center point. To list the four vertices.

Q: Using the the derivative method power rule. How come the answer is 2t^-3? Instead of 2t^1?

A: Given: f=-1t2 We are required to find: The derivative of f

Q: Follow the Steps to Successful Curve Sketching to sketch the graph of f(x)=-4 Show all stens

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Q: In(1 + √x) √x s dx

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Q: Solve each of the given triangles (i.e. find the lengths of the missing sides). Parta) Part b) 160°…

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Q: Given below are descriptions of two lines. Line 1: Goes through (-4,10) and (0,4) Line 2: Goes…

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Q: Explain why the function is discontinuous at the given number a. (Select all that apply.) x2 - 2x x2…

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Q: 11. Use a table to find the Taylor polynomial P3 (x) for f(x) A. B. P3 (x) = Use the series to…

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Q: 4. Determine the vertex of the parabola y 2 2x + 15x using Calculus.

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Q: 2. S dx x√x4-4

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Q: Find the equation of the line perpendicular to x = 3 through the point (-4, 7)

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Q: fip da ॥ 72 fi 2r+39 e

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Q: x2 - 4 3 dx

A: The given integral is: I=∫x2-4x3dx

Q: Compute the partial sums S2, S4, and S6 of 1 1 1 1 + + 12² 24² 36² 48² (Use symbolic notation and…

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Q: Ja 3 x√x - 2dx

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Q: Describe the interval(s) on which the function is continuous. (Enter your answer using interval…

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Q: 4. Show that det(AB) = det(A)det(B) for A ===[₂]

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Q: Part b must have some form of an answer right? It doesn't give me the option of DNE or anything, so…

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Q: Given 2sin(x)= − 1, on the interval 10, 2], what is the value of x? 7개 11개 이뽕 {픔. ㅠ (픔·품] 6 6 7개 5개…

A: Solving the problem

Q: Find an equation for the plane tangent to the given surface at the specified point. x = 2u₁ y = u² +…

A: We have x=2u, y=u2+4v, z=v2, at (0,8,4). Then we have to find an equation for the plane tangent to…

Q: A toy ball is thrown into the air from the top of some bleachers which are 5 feet above the round.…

A: Given    h(1) which means after 1 sec height of ball will be 13 feet

Q: 0. 23. L₂ (x² + x) dx

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Q: SKETCHPAD Question 16 What unit vector is in the same direction as v = 2i - 4j?

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Q: dy 3) Using the function y=f(x)=x², state which of the following uses of the notation: dx d and are…

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Q: Find the radius of convergence of the power series 1 xn 3n+ (−2)² (n +1) n=0

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Q: 8 3 + 8 2 + 18 3 3 + 8 3 +. ...

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Q: 1. Determine the complete solution of the given differential equation y"+y' - 2y = 2x - 40cos2x. Use…

A: The given differential equation is; y''+y'-2y=2x-40cos2xSolve by method of undetermined…

Q: Let f(x) = x³ 3x - 1.5. Determine whether the Intermediate Value Theorem can be used to show that…

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Q: In Calculus you will see the symbol y'. Treat y' as a variable and solve the equation for y. 6y²y +…

A: To solve the following equation for y'. 6y2y'+30xy+6x2y'=5y2+25xyy'

Q: c) Compute the fastest total time Nadia takes to the bus stop if Alania walks side walk first then…

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