How many critical points the following function has, f(x, y) = 4x² - 2xy + 2y³? Select one: 0 2 O 0 1 None of them

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Q: Find linearly independent functions that are annihilated by the given differential operator. (Give…

A: The characteristics equation is (m-3)(4m+5)=0. So,                   m-34m+5=0⇒m-3=0  or…

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A: We can solve as follows

Q: tor. f(x,y)= In (8+3x²+3y²); P(3,-1); (3.2) d the gradient of f(x,y) = In (8+3x²+3y²). xx,y)=

A: Topic:- application of derivatives

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Q: L1Q7. If the degree of a polynomial function is even and the leading coefficient is positive, then…

A: Given; Degree=even   Leading coefficient= positive.

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Q: (a) Find the volume of the solids generated by revolving the region bounded by the curves y=z²+1,…

A: To solve the following problem of finding volume using washer method.

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Q: State the range of f(x): {y € Ry> 4 -3} {ye Ry - 4 3 {y € Ry#0} {y € Ry>0} } = 1 3x +4'

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Q: Find the critical numbers, the intervals on which f(x) is increasing, the intervals on which f(x) is…

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Q: Find the indicated Trapezoid Rule approximation to the following integral. S²4 sin S²49 T 4 sin dx…

A: We have to find the Trapezoid Rule approximation to the integral ∫024 sin π2x dx using n=6…

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Q: Use appropriate algebra and Theorem 7.2.1 to find the given inverse Laplace transform. (Write your…

A: Given:      L-1ss-3s-4s-12 Taking Partial fractions of  ss-3s-4s-12

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A: We need to find S'(t).

Q: Evaluate (2x - y) dx + (x + 3y) dy. C: arc on y = x5/2 from (0, 0) to (4, 32)

A: Solution of given question is written in below steps.

Q: Use implicit differentiation to find y' for the equation below and then evaluate y' at the indicated…

A: It is given that, y2+3y+2x=0  Find y' and evaluate at point (-5, 2).

Q: Use the indicated change of variables to evaluate the double integral. JS4 4(x² + y²) da X = = 1/2…

A: Let's solve given double integration by changing variables.

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Q: b. (1) (x) c. (fog)(x) d. (gof)(x)

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Q: Find the exact values of the six trigonometric ratios of the angle 8 in the triangle. sin(8) "…

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Q: tank

A: Please refer to the image below

Q: Let V₁, V₂, and v3 be vectors in a vector space V, and let T:V R³ be a linear transformation for…

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Q: 2x, y 3 and 0. Sketch the region R and evaluate the double Let R be the region bounded by y X =…

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Q: The cost of producing z units of a commodity is given by C(z) = 140 + 15z - 0.8a marginal cost…

A: We will find the marginal cost function.

Q: Use the Root Test to determine convergence or divergence (or state that the test is inconclusive).…

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Q: If f(x, y) = = Select one: O True O False x² + 2xy + y³ 2x + 2y 3y² + 2x '(x² + 2xy + y³)²¹ (x² +…

A: As we know the expression for ∇fx,y. ∇fx,y=i∂∂x+j∂∂yfx,y=∂fx,y∂xi+∂fx,y∂yj   Given: fx,y=1x2+2xy+y3

Q: 5) (10 ptos) Determine los puntos críticos de ƒ(x) = ²x³ + x² – 2 2x

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Q: 1. Find the critical points of the function 2 f(x, y) = x² + 4xy.

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: Determine where, if anywhere, the function f(x)=x3+9x2−48x+2f(x)=x3+9x2−48x+2 is not changing

A: This is a application of derivative problem

Q: 3) y(³) − y(¹) = cos(2x). -

A: Giveny(3)-y(1)=cos(2x)To solve differential equation:

Q: Determine all values of x at which the function f(x) O discontinuous at -1 and 1 O discontinuous at…

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Q: 4. Which of the following differential equations has the slope field below 22 ܟ O dy dx dx dx ܔܔܔ…

A: The given slope field is for dydx = -xy . Because slope y'(x) of the solution y(x) is determined…

Q: A $47,500 loan was cleared in 5 years by setting up a sinking fund that was earning 3.25% compounded…

A: Let's find sinking fund deposits and interest.

Q: Obtain an exponential function in the form f(t) = Aert. HINT [See Example 5.] f(t) is the value…

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Q: 2. f cos²xsin² xdx

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Q: 1.73 × 10-3/7.8 × 10 Express your answer to the correct number of significant figures. —| ΑΣΦ BERERT…

A: The solution is given below

Q: The function z = Select one: O True O False f(x, y) has a local maximum at the critical point (3,-1)…

A: Given z=f(x,y) D(3,-1)=4 and fxx(3,-1)=-5

Q: Use Definition 7.1.1, DEFINITION 7.1.1 Laplace Transform Let f be a function defined for t > 0. Then…

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Q: For the function f(x) = sinx, where a = find the following. 6 a. Find the Taylor polynomials of…

A: Please see the below picture for detailed solution.

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A: Starting from dashed graph let y=f(x)   Step-1 : Taking mirror reflection about  the horizontal…

Q: Evaluate the integral 2 2-x [1² 0 0 xdydx.

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Q: A cable hangs between two poles that are 70-ft apart. The two poles are both 40 foot high. Sag is…

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Q: (a) Find the area of the region bounded by the given curves a x = e.

A: Solved below.

Q: Given: f(x) = x³ – 6x² − 15x + 7. Find the LOCAL MINIMUM point of f (x). A. (5, ƒ (5)) B. (−1, ƒ…

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Q: 2. A differential equation that is a function of x only O will produce a slope field with parallel…

A: Here, given that the differential equation is a function of x only. So, dydx=f(x)⇒y=F(x)+C, where…