Find the component form of v given the magnitudes of u and u + v and the angles that u and u + v make with the positive x-axis. |u|| = 1, 8 = 45° u+v=√√2,6 = 90° V=

Q: How many critical points the following function has, h(x, y) = 1 + x³ + x + xy²? Select one: O None…

A: We can find the answer as below.

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

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Q: Determine whether Rolle's Theorem can be applied to f on the closed interval [a, b]. (Select all…

A: NOTE: Refresh your page if you can't see any equations. . Rolle's theorem is  If a function f is…

Q: Find a vector-valued function whose graph is the indicated surface. The cylinder 9x² + y² = r(u, v)…

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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: The point (0, 0) is the critical point of the function f(x, y) = Select one: O True O False x²y 2 +…

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Q: Please

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Q: Evaluate the integral using an appropriate substitution. NOTE: Enter the exact answer. x3 (3x²+2)³ J…

A: Given: I=∫x33x4+23dx     ...1   As we know that; The Power Rule: ∫xndx=xn+1n+1+C ; n≠-1

Q: Find f'(x) and find the equation of the line tangent to the graph of f at the indicated value of x.…

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Q: Let f be a function defined for t≥ 0. Then the integral is said to be the Laplace transform of f,…

A: The given function, ft=-1,0≤t<11,t≥1

Q: Evaluate the integral by applying the following theorems and the power rule appropriately. Suppose…

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Q: Question 1 Consider the matrix A- - (a) (b = 64 -1 1 -1 0 3 -2 -2 2 1 Compute the adjoint matrix…

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Q: Find the absolute extrema of the function on the closed interval. f(x) = 7x² + 2, [-1, 2] -(0,2…

A: The answer is given below:

Q: Find the work done by the force field F in moving an object from P(-3, 7) to Q(7,5). 2x F(x, y) = -

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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: 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: Find the relative extrema of the function, if they exist. 3) f(x)= 3x4 + 16x3 + 24x2 + 32 4) f(x) =…

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Q: dt || y whent = 0, y =

A: Please refer to the image below

Q: The half-life of cobalt 60 is 5 years. (a) Obtain an exponential decay model for cobalt 60 in the…

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Q: Question 3. (a) (b 2 1 0 -1 Evaluate the determinant of the matrix -1 1 Use the Cramer's rule to…

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Q: (2) = [ (t² − 1) dt (b) f(x) =

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Q: Question 2 [2 Consider the matrix B= = (a (t -1 2 1 -1 2 1 -1 -2 0 Use the cofactor exapansion to…

A: We have to find the determinant.

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: 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: 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: Solve the problem. 15) Let f(x) = ex. Round to 6 decimal places as needed. a) Find the linearization…

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Q: Use the given graph of f'(x) to find the intervals on which f(x) is increasing, the intervals on…

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Q: 6. g(u) 5 4 3 ANA -4 Based on the graph above, find the following: Amplitude: Period: Midline:…

A: Please see the below picture for detailed solution.

Q: The value of the integral Select one: b. None of these 5 4 d. / c. [ [²x² 7/2 x²y³ dx dy is:

A: This is a double integration problem

Q: Suppose (1, -1) is a critical point of a function f with the continuous second derivatives. If fxx…

A: As we know from the double differentiability test, When rt-s2>0 and r>0 then minima will…

Q: r-Check Library nts adebook Schedule n e Resources e Options Quick Guide unication Tools F Ostly…

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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: 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: Graph the function by first finding the relative extrema. 1) f(x) = x3+4x2-x-4 24 20 16 12 8 28 55 8…

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Q: 3. A bucket that weighs 3 lb and a rope of negligible weight are used to draw water from a well…

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Q: xdx + (y − 2x)dy = 0

A: According to our guidelines , we can answer only first question. Kindly re-post other remaining…

Q: Evaluate the integral and check your answer by differentiating. NOTE: Enter the exact answer. 3 S[ ²…

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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: 1. Which of the following values would be obtained using 10 circumscribed rectangles of equal width…

A: The integral is  ∫01 x2 dx

Q: 9. Find if x (t) = t + sin(t), and y(t) = t - cos(t). doe

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Q: 1) (. B enclosed by the curves Find the exact area of the region y=x² and y=x+ 20. Write your answer…

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Q: Find a vector-valued function whose graph is the indicated surface. The plane z = 4y r(u, v) =

A: Solution ) the plane      z = 4y   Let's make substitution  x =u , y = v  Hence  z = 4v   r ( u, v)…

Q: Find y' and the slope of the tangent line to the graph of (3x-2y)5 = 2y2-9 at the point (1,2). y'=0…

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Q: 2. Integrate using an appropriate method. 1 PVR-36° dr

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Q: What is the symmetry of f(x) = 2x4 - 5x² +9? Select one: a. odd b. neither O C. even

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

Q: Determine whether or not the vector field is conservative F(x,y) = 18x²y²i + 12x³yj conservative O…

A: NOTE: Refresh your page if you can't see any equations. . compare this vector field with  so here…

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

A: As per guidelines we can answer only one question at a time, so if you need more answers kindly…

Q: The maximum rate of change of the function 1 f(x, y) = at the point (1, -2) happens in direction of…

A: I have find the direction and value of maximum rate of change of given function and say that given…

Q: A farmer is building a fence to enclose a rectangular area consisting of two separate regions. The…

A: Given problem:- A farmer is building a fence to enclose a rectangular area consisting of two…