The maximum rate of change of the function 1 ----> at the point (1,-2) happens in direction of < -1,-1 > and with the value of √2. Select one: f(x, y) = True

Q: Q2. Consider the function f: f(x, y) = x² - 4x + y² − 6y ] Find all critical points of f. Find the…

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Q: Let f(x, y) = 2x² + 3y2, then (2, 3) is not a critical point of f(x, y). Select one: True False

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Q: Evaluate the integral using an appropriate substitution. NOTE: Enter the exact answer. x³ (3x4 + 2)³…

A: We need to integrate ∫x33x4+23dxSubstitute 3x4+2=tDifferentiate w.r.t t12x3dx=dtNow∫112t3dt ---{1}

Q: The directional derivative of a differentiable function f(x, y) in the direction of a unit vector u…

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Q: Evaluate the integral using an appropriate substitution. NOTE: Enter the exact answer. [e³ 34x dx =…

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Q: Q1) () points) a) Sketch the region of D = {(x,y) :-√√4-y≤x≤ ¹,0 ≤ y ≤ 4} b) Reverse the order of…

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Q: dz Find given: dt z = xe²y, x = t³, y = - 5 + 6t dz dt ||

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Q: Graph the given function using a chart of values. (Use -3 ≤ x ≤ 3.) h(x) = -3(2-x) y 30 y 30

A: Please refer to the image below

Q: Solve the given initial-value problem. y(x) = y" - 81y = 9, y(0) = 1, y'(0) = 0

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Q: a) [ : Find the volume of the solid obtained by rotating the region bounded by the lines «<math y =…

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Q: If V f(x, y) = (x² - 1,√y-1), then f have two critical points (1, 1) and (-1, 1). Select one: O True…

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Q: Find the radius of convergence of the series. 5 OR=7 OR = 1/ OR=1 OR=00 OR=0 7"x" 1 (n + 1)"

A: We need to find radius of convergence.

Q: Q2) [ Given the function f(x,y)=x²-6x+y²-6y+8 a) [ Find all critical points of f. b) Find the…

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Q: Describe the region D enclosed by:y=2, y=2r+2 and y=-2x + 2 as a region of type II: Select one: O D=…

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Q: 13.) 2 automobiles start from the point A at the same time. One travels west at 60 miles/h and the…

A: Given Velocity of one = 60 i Velocity of second = 35 j

Q: What is the value of the integral. Select one: 64 O 16 O None of these 0 32 8 CC 00 2rydydz? D 03 S

A: As per bartleby guidelines we only give first question answers.  Please repost for other parts.

Q: Find the natural domain and graph the function. f(x)=√√-x-10 What is the natural domain of the…

A: In this question, we want to find the domain of the given function and graph the function.

Q: The Integral fi fig(z,y) dyda can be written as: 21-9(x,y) dzdy Select one: O True O False

A: We can solve this as follows:

Q: Which of the following functions is symmetric about the y-axis? A.f(x) = x4 - 4 B.f(x) = x5 - 4

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Q: 4. Given x = 2 cos (6) and y = 2 sin(0), for 8 € [0, π] Eliminate the parameter to find a Cartesian…

A: Here, the given parametric equation is: x=2cos(θ), y=2sin(θ), for θ∈[0,2π]

Q: Classify the following diferential equations. Write the order, linearity and the homogeneity of the…

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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: The graph of y = f(x) is shown below (dashed curve). Manipulate the green draggable points to obtain…

A: Given data ÷ Graph of y=fx is shown with dashed line curve. We need to graph  y=2fx+1-4

Q: Question 1 The region D is enclosed by + y = 2, ya, and y-axis. Give D as a type I region, and a…

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Q: egral f x²+x+2 dx (x-1)(x²+5)

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Q: 6. Find the area of one loop of the polar curve r = 2 sin 30

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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.

Q: f(x) = 5x + 21, [-4, 4] , the Mean Value Theorem can be applied. f is not continuous on [a, b]. .f…

A: Topic:- function  Mean value theorem :-  Stats that    The function f(x) is continuous over the…

Q: Find the equation for an exponential function that passes through the pair of points given below.…

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Q: a) Determine if the geometric series 8n-1 90+1 n=1 is convergent or not, and find its sum if it is…

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Q: The function f(x, y) = 2x³ - 6x + 6xy² has: Select one: O One minimum One maxima and one saddle…

A: Topic:- application of derivatives Note :- as per our guideline if more than one question uploaded…

Q: III-Déterminer la dérivée de : a) f(x) = lnx lnx + 1 III- Determine the derivative of: ex +1 J b)…

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Q: Choose the gradient of the function \(f\) defined by f(x y) √1 (4x 5y)². O None of the others 4x+5y…

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Q: Find the domain of the vector-value function r(t) = www Domain: {tt # MORA 4t4, t², 1 (t - 2)5

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Q: Evaluate the iterated integral: - 7 -X = S S e-* dydx е 8

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Q: What we know: outer green square box has a side length of 10 inches, inner square has a side of 6…

A: Concept: Area of the square: A=side2 The diagonal of the square is : d=2side Area of circle: A=πr2…

Q: Evaluate the integral and check your answer by differentiating. x² +8x4 1 x6 1² dx +C

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Q: 1. Integrate using an appropriate method. [2si 2 sin³(r) cos² (r)dr

A: The given integral is: I=∫2sin3xcos2xdx   As we know that; The trigonometric identity; sin2x+cos2x=1…

Q: √x dx for n=4 is equal to Using Simpson's method 0 Blank 1 (use 2 decimal places with proper…

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Q: The gradient vector of g(x, y) = at (√√2,-1) is Vg(√2, -1) is equal to Select one: O True O False -

A: Given: The gradient vector of g(x,y)=x22-y22 at (2,1) is ∇g(2,1) is equal to &lt;2,1&gt;

Q: [²² y dydx = 2. Select one: O True O False

A: Select one

Q: 2. If y is the solution of the initial value problem = 3(y - 1)(y-2) with y(1) = 3, what is lim…

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Q: Solve the problem. 28) A kitchen remodeling company determines that the marginal cost, in dollars…

A: In this question we have to find the cost of installing an extra 9 feet of countertop.

Q: f _____________, then the graph of the polynomial function is symmetric about the origin. A.f(x) =…

A: Note that, a function that is symmetrical with respect to the origin  is called an odd function.

Q: Q1 (2 Let R be the region bounded by y = 0, y = x², x = 1. a) Sketch the region R. b) Evaluate the…

A: Here, the region of integration is: y=0, y=x2,x=1

Q: Find a closed form for the infinite arithmetic sequence given by the recurrence system:  x1 = -1,…

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Q: The function f(x, y) = -2x² + 4y? - 11 has a local minimum at the point (0, 0). Select one: O True O…

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Q: he normal vector to the tangent plane for the surface point (1, 2, -1) is: Select one: None of them…

A: topic:- application of derivatives

Q: e -1-21 (22+3) dz Ans 17+19 ng the path x=2t+1₂ Y = 4t²_t_2 ost

A: I= ∫1-2i3+i(2z+3)dzalong path x =2t+1,y=4t2-t-2z=x+iyz(t)=2t+1+i(4t2-t-2)dz=…

Q: Find the marginal profit function if cost and revenue are given by C(x) = 157 +0.7x and R(x) = 8x…

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