14. Find all the critical points of the function f(x, y) = sin(x + y) and determine if they are points of local maxima or local minima or saddle points.

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A: Given data The equation of paraboloid is, z=x2+y2. The limits of the square is 0≤x≤3, 0≤y≤3.

Q: Solve the following initial value problem: dy t dt (3²,-²) y5 y(t)= | + = 0, y(1) = 1. 2y4 I

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Q: 5. Find the maximum height above the x-axis of the polar curve r = 2+2 cos(0).

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Q: If position is given by p(t) = -1² + 5t, what is the veloci v(t) at t = 2? ov(2) = 2 ov(2) = -1

A: note :- since  you have asked multiple asked questions but accoeding to bartleby  guidelines i unly…

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Q: Direction: Analyze the given problem. Show your complete and detailed solution (Given, Unknown,…

A: Solution: Given data, Let the width and length be x and y respectively. area = 2000 Sq.ft.…

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Q: Suppose y = √2x + 1, where x and y are functions of t. (a) If dx/dt = 9, find dy/dt when x = 4. dy X…

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Q: Volume = --1 1,0

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Q: Compute the following limit: lim x→∞ e3x

A: Use the Taylor’s series extension of e3x and then simplify.

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Q: Locate the critical points of the following function. Then use the Second Derivative Test to…

A: The given function is;  f(x)=-x3+15x2.

Q: 2. a) Estimate the instantaneous rate of change of the function at the tangent point (7,9) indicated…

A: Given,

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Q: 3 Y +22= 3 Y+2=5 2X, +3 Y+52=0

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Q: Evaluate the iterated integral T by reversing the order of integration. rocs(2y²)dy) dx,

A: Please see the below picture for detailed solution.

Q: Suppose that f(x, y) = √√5² - x² - y² on the domain D = tr=5 O = {(x, y) | x² + y² ≤ 5²}. Q Then the…

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Q: The line ℓ is given by the equations x −2y + z = 2 and x + y −3z = 4. That is, ℓ consists of all…

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Q: me: 3. What does the lim h 0 f(x+h)-f(x) h Date: 2 =- - 4 indicate about the graph of the function…

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Q: count in a bacteria culture was 900 after 15 minutes and 1800 after 30 minutes. Assuming the count…

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Q: the instruction says you should use miscellaneous substitution! please edit the answer

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Find the slope of the tangent line to the curve defined by 9x¹ - xy - 6y² = -16 at the point (2,5)…

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Q: You've decided to sell sweatshirts for the upcoming game. You project that at a price of $29.04 per…

A: It is given that, At the price of $29·04, 180 shirts are sold and at the price of $21·84, 280 shirts…

Q: You are in charge of erecting a radio telescope on a newly discovered planet. To minimize…

A: Given: Mx,y,z=12x-y2+xz+240The radius of the spherical planet is 12 unit. Hence, x2 + y2 + z2 =…

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Q: miscellaneous

A: We have to integrate according to the given information

Q: c) Derivatives of trigonometric function and inverse trigonometric functions 6) Differen...... 7)…

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Q: Find the volume V formed by rotating the region enclosed by the curves: y³ = x and x = 4y with y ≥…

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Q: Please help (41-45)

A: Here we have to find the derivative.

Q: shells: (A) The method of cylindrical shells: The circumference of a typical shell = The volume V =…

A: To solve the following problem

Q: Find the limit. lim (csc (2x) - cot (2x) + cos (4x)) = (Type an exact answer.) X→0*

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Q: 8. Complete two iterations of Newton's Method for the function f(x) = x² −7, using the initial guess…

A: Newtons method to find solution

Q: J. •[ 2 √ x² + 1 dx

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Q: Evaluate the integral by interpreting it in terms of areas. 6² ( 1² x - 2) αx -X dx

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Q: Using the given graph of a curve y = f(x), determine whether each of the derivatives given below are…

A: Here we have to observe the graph.

Q: 10. Suppose that you have the following table of values for a function: f(x) 100 X 0 1 2 3 4 71 50…

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Q: If f(t) = (t² + 6t+4) (2t² + 2), find f'(t). Find f'(3). Question Help: Video Message instructor…

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Q: Problem 1 A large pizza of radius 15 in. is sliced into 8 delicious equal pieces (the normal way a…

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Q: If f(x) = 3 x-3 7 and g(x) = 7x³ + 3, are f(x) and g(x) inverse functions?

A: The functions f and g are inverse functions for each other if and only if f∘gx=g∘fx=x

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A: Marginal revenue is the rate of change of the revenue function. Marginal revenue is denoted by…

Q: Suppose that f(x) . (If an answer does not exist, enter DNE.) (a) Find all partition numbers of…

A: As per our company guidelines, we are supposed to answer only the first 3 sub-parts. kindly repost…

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Q: Show that the scalar field = 1/R], which is defined everywhere except at the origin, is a potential…

A: If f is a function then ∇f=fxi+fyj+fzk. f is a potential function of F if ∇f=F

Q: e volume of the frustum of a right circular cone with height h = 71, lower base rac

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