2. Which definite integral approximation formula is f(x) dx = Left rectangles Right rectangles Average value O Trapezoidal rule Yo+Y₁+Y₂+3+...+Yn-1]

Q: The directional derivative of f(x, y) = e²y - x at the point (1, 2) in the direction indicated by…

A: In this question, We want to find the directional derivative in the given direction.

Q: Ise spherical coordinates to find the volume of the region bounded by the sphere p= 20 cos p and the…

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

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Q: n 1 ² Σ (sec (2 + ²) - 2 (2 + ² +)) - nxn i=1 3. Express lim as a definite integral, f(a)da.

A: This is a integration problem

Q: 2²2 +2²2² = 12 25 (a) Find the vertices, foci, and eccentricity of the ellipse. (x, y) = (-5,0 (x,…

A: The equation is  x225+y29=1

Q: Choose the area of the region enclosed by: x = 0, y = 0, y = -x + 1. Select one: y-1 LL" dady O None…

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Q: Consider the function f(x, y) = y ln x - x ln y - . a Find the directional derivative of f at the…

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Q: What bearing and airspeed are required for a plane to fly 700 miles due north in 3.5 hours if the…

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Q: The double integral √ √ ₁ (3. R (3x² + 2y), where R = [1, 2] × [-1, 2] is equal to Select one: O 18…

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Q: How many critical points the following function has, g(x, y) = x³ + x + xy²? Select one: CO None of…

A: Using partial derivative with respect to x and y ,

Q: f SSR5e -27 sin(5x)y cos(2y) dxdy = f, 5e-2¹ sin(5x) dx f2, y cos(2y) dy where R = [-1, 1] x [1,2].…

A: This is a double integration problem

Q: Create a table of values for the function and use the result to estimate the limit. Use a graphing…

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Q: Find a formula for the general term an of the sequence, assuming that the pattern of the first few…

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Q: egral f x²+x+2 dx (x-1)(x²+5)

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Q: ether yp₂ (x) = x is a particular solution g DE or not. y" + 4y = 4x.

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Q: 2. Find the rate of change of the function f(x, y) = x² sin y at the point (1,) in the direction of…

A: To find out the rate of change in the direction of the given vector.

Q: Question Determine the direction in which the graph of the following parabola opens. f(x)=(x-2)² – 5…

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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: Model the data using an exponential function f(x) = Abx. f(x) = X f(x) 0 1 128 64 2 32

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Q: 1. Find the gradient of the function f(x, y) = x² sin y. 2. Find the rate of change of the function…

A: The given function is;  f(x,y)=x2 Siny.

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

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Q: Use the double integration find the area of the parallelogram whose vertices are A(1,0), B(3,1),…

A: Area of parallelogram

Q: Find the relative extrema of the function and classify each as a maximum or minimum. -2)2/3 5) f(x)…

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Q: Choose the gradient of the function : f(x, y) = ex² Select one: O None of these ○ (6ye+²+³y², 2xer²…

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Q: 1 Evaluate the integral ¹ x xdydx Select one: O -1/10 O None of those O 1/10 O -1/5 O 2/5

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Q: Find an equation for the ellipse that satisfies the given conditions. Foci: F(0, ±2), vertices: (0,…

A: Given, Foci: F(0,±2),  vertices: (0,±5)

Q: Solve the IVP: y" - 6y' + 8y = 0, y(0) = C

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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: Find the volume bounded by 3x+2y+z=12 bounded by x=0, y=0, z=0

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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: The gradient vector of the function f(x, y, z) = ln(yz) + x² is: Select one: (2x, /, // ) (2x, -, -…

A: gradf =∇f =i∂∂x+j∂∂y+k∂∂zf .

Q: Question 2 el: Determine whether the following functions are linearly dependent or linearly…

A: The objective of the question is showing that given functions are linear dependent or independent.

Q: Which of the below double integrals has the following region? -1 5 4 3- 2 -1 0 Select one: None of…

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Q: : Find the orthogonal trajectories of the family of curves y4 = kx³. (A) 2y³ + 3x² = C (B) 2y³ + 2x²…

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Q: Choose the area of the region enclosed by the curves -6 4x 0 x=0, x=6, y = 4x², y = 4x. 4x2 6 SO SAX…

A: Given.

Q: True or False If determinant of matrix A is equal to 1, then the transposed matrix of cofactors of…

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Q: Given the function f(x, y) = 2-x² + 2x² - y² a. Find the critical points of f, and determine which…

A: Maxima minima, directional derivative

Q: Find an equation for the ellipse whose graph is shown. y 0 (10,5) 15 X

A: Consider the ellipse  Consider the graph

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

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

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

Q: The Integral f fyr² dyda can be written as: Select one: ọ Sổ Sing dady O None of the others Of fyr²…

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Q: dl ) Verify that y = C₁ cos(3x) + c₂sin(3x) is a solution of 2); A) (::. - y" +9y = 0 B) {….. y' +…

A: Solution

Q: How long, to the nearest year, will it take an investment to triple if it is continuously compounded…

A: We can find the required year in the following steps.

Q: Find an equation for the hyperbola that satisfies the given conditions. Foci: (±5, 0), length of…

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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: The maximum rate of change of the function 1 ----> at the point (1,-2) happens in direction of and…

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Q: 2. Differentiate the following: (a) y = x²z

A: The given expression is: y=x2x   ...1   As we know the Product rule: f·g'=f'·g+f·g' The Power Law:…

Q: 33) (x5-2x4)4 (5x4-8x3) dx

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Q: Give an example of a function of the variable x that has a: a) vertical asymptote in x = 2. b)…

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Q: The Integral ffyr² dydx can be written as Select one: O So yx² dady Spa

A: Need to change the order of the integration and select the correct option. Given information: The…