1. Find the gradient of the function f(x, y) = x² sin y. 2. Find the rate of change of the function f(x, y) = x² sin y at the point (1,5) in the direction of the vector v =< −6, 8 >.

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: Recently, a certain bank offered a 10-year CD that earns 2.16% compounded continuously. Use the…

A: We have to find gross amount

Q: Solve the length of the unknown side. Round each answer to the nearest tenth. 21 La ins 120000 2…

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Q: Use sigma notation to write the sum. 4 [G)²-1])+ N" i=1 X [(4)²-“() X

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Q: Find the average temperature in the box D = {(x,y,z): 0≤x≤ In 3, 0sysin 9, 0≤z≤ In 27) with a…

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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: Given the function h(x) below, select the answer choice(s) which correctly decompose h(x) into…

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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

Q: 30. Paolo's wife Cristina is not happy about the play area he proposes to build for their children.…

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Q: -4 - Find the derivative for the function f(x) = (5x−4+ 3x + 7) (8x−³ − 7x + 10) 5. Do not simplify…

A: Given, f(x)=5x-4+3x+78x-3-7x+105

Q: (d) Find the volume of the solids generated by revolving the region bounded by the curves y = 2x -…

A: Solved below

Q: Consider the following functions. f₁(x) = x, f₂(x) = x², f3(x) = 6x - 4x² g(x) = c₁f₁(x) + c₂f₂(x) +…

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Q: Sequences have many applications in mathematics and the sciences. In a recent paper³ the authors…

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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: Find the cross product a x b. a ++kb-i+2j - 3k 10 Verify that it is orthogonal to both a and b. (a x…

A: Consider the vectors  a=12i+13j+110k,    b=i+2j-3k

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

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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: Determine if the critical points of the function f ( x ) = x³ + x² - x - 2 are maximum or minimum…

A: The given function is: fx=x3+x2-x-2   As we know that; To calculate the critical point, f'x=0.

Q: Which term in the expansion of 2x is a constant?

A: 12x3-x58

Q: 8) Use the functions f(x) = x² and g(x) = √2-x to find the specified function its domain: a.…

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Q: The acceleration of an object (in m/s²) is given by the function a(t) = 5 sin(t). The initial…

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Q: Find the area of the triangle. (Round your answer to one decimal place.) 2

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Q: - Evaluate sin x dx using 3 i. Trapezoidal rule ii. Simpson's rule iii. Simpson's rule, taking n = 6

A: We have to evaluate ∫0π2sin x dx. Here a=0 and b=π2=1.570796 Given n=6 ∴ h = b-an = 1.570796-06 =…

Q: Given: f(x) = 2x³ + 6x² f(x) on [-1,3]. A. 165 B. 109 C. 57 D. 51 E. NO correct choices O O OO C D E…

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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: Find the transition points. f(x) = x(17- x)¹/3 (Use symbolic notation and fractions where needed.…

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Q: 3) Find the Taylor series for the function g(x) = x²e³x+¹ centered at a = 1.

A: To find the Taylor series for the function gx=x2e3x+1 centered at a=1.

Q: A tank contains 150 gal of fresh water. A solution containing 5 lb/gal of soluble lawn fertilizer…

A: answer is in next step . please give a like!!

Q: Which of the following is NOT a subspace of M22? O O W is the set of matrices of the form and z are…

A: Here is the answer:

Q: A triangular parcel of land has sides of lengths 330 feet, 650 feet and 732 feet. a) What is the…

A: We can answer both the question as below.

Q: 2. The slope of the tangent line to a curve at any point (x, y) on the curve is. What is the…

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Q: L4Q15. In a display, there are 50 toys in the first row, 45 toys in the second row, and so on in an…

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Q: Find an equation of the tangent plane to the parametric surface + = Z= Note: Your answer should be…

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Q: Evaluate the line integral along the given path. ds [ (x² + x² +2²) 0₂ C: r(t) = sin(t)i + cos(t)j +…

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Q: Using Lagrange multipliers, find the maximum and minimum values of the function f(x, y, z) = 8x - 9z…

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Q: Given the triangle 28/ 11° X 28 final answer to 4 decimal places. I= find the length of side using…

A: Explanation of the answer is as follows

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

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Q: A machinist is required to manufacture a circular metal disk with area 934 cm². Give your answers in…

A: Concept: The area of the circular disk is  A=πr2 Where r is the radius of the circular disk The…

Q: Use the Ratio Test to determine whether an 15" n! Evaluate the following limit. an+1 lim n→∞ an an…

A: This question can be solved using the concept of test for convergence.

Q: Find the slope and y-Intercept (if possible) of the line. (If an answer is undefined, enter…

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Q: Evaluate the iterated integral: I 7-x X -SS e dyda 8 7 2

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Q: Q1. If g = xy — yz — zx and F = x²y ī − 2 y²zī – z²x k, find F. grad g and cross product of F and…

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Q: = Find the area A of the region that is bounded between the curve f(x) = ln (x) + 1 and the line…

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Q: Use the functions below to find the given value. f(x) = x 2 8 g(x) = x³ (g¹¹) (-2) = |

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Q: Find the work done by the force field F on a particle moving along the given path. F(x, y, z) = yzi…

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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.

Q: Evaluate the line integral along the given path. (Round your answer to two decimal places.) Jox xy…

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Q: 8.) A triangle has a base of 12ft long and an altitude of 8ft high. Find the area of the largest…

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Q: Calculate the volume under the elliptic paraboloid z = 4x2 + 6y2 and over the rectangle R = [-2, 2]…

A: The solution for the above question is shown below.

Q: Consider the basis S = {V₁, V₂] for R2, where v₁ = (1, 1) and v₂ = (1, 0), and let T:R2 R2 be the…

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