Find the minimum and maximum values of the function subject to the given constraint f(x, y) = x² + 4y², x+16y=5

Q: Find an equation for the plane that is tangent to the given surface at the given point. z= √y-x…

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Q: Find an equation for the tangent line to the curve given parametrically by y(t) = 4t² + t - 1 2t…

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Q: 105x2,5 x 2

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Q: Find the curvature of r(t) = √√6ti + e¹j + e¯ªk at point P(0, 1, 1). 1 4 X

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Q: 2x^2(y)+3xy^2−2x=−6  at the point (3,0)

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Q: 8. y = sin(tan¹ 3x)

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Q: If 4x² + 5x + xy 2 and y(2)= differentiation. = Question Help: Message instructor 12, find y' (2) by…

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Q: Determine whether the series converges. 5 sin² k k! (3) (4) k=1 4k-2k+6 18k+k-8 WI

A: Given series  (3) ∑k=1∞5sin2kk!   (4)∑n=1∞  4n2−2n+68n7+n−8

Q: 1. Determine whether or not the following relations are functions. If the given relation is a…

A: As per our guidelines we can answer only 1 question, so kindly repost the remaining questions…

Q: Sketch the graph of a function f having the given characteristics. (Select the correct graph.) f(0)…

A: Given query is to graph the function with indicated characteristics.

Q: Problem 3. We want to estimate (²1/1 X dx. We will use the right sum, left sum, midpoint rule and…

A: Let's calculate L(2),R(2),M(2) and T(2).

Q: Find all values of t, -/2 < t </2, for which the tangent line to the graph of x(t) 4t+3 tant, y(t) =…

A: NOTE: Refresh your page if you can't see any equations. . the given parametric curve is

Q: If -5xy - y² - 3x³ dy that = dx = 1 and it is known 5y+9x² -5x-2y' find all coordinate points on the…

A: We are given a curve  -5xy-y2-3x3=1   and we are also given that dy/dx = (5y+9x2) /(-5x-2y)  ...A We…

Q: The height (feet) of a ball launched in the air t seconds after it is launched is given by: f(t) = -…

A: Given: Now, the velocity of the ball will be f'(t)=-32t+319. And when it strikes the ground is…

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Q: The height (feet) of a ball launched in the air t seconds after it is launched is given by: f(t) = -…

A: Topic- Application of derivatives We are given, height of a ball launched in the air t seconds after…

Q: Find f'(− 3) if f(x) = 8 3x.

A: Given query is to find indicated derivative.

Q: Question 1 Part A Complete the square for the quadratic f(x) = x² - 5x. ]× ›)²-([ f(x) = (x + ( […

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Q: Consider the given function and the given interval. f(x) = (x − 7)2,    [5, 8] (a) Find the…

A: The given function is: fx=x-72, 5,8 To find: (a) The average value fave of f on the given interval

Q: Find the exact length of the curve. y = 2x3/2, 0≤x≤6

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Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y.…

A: Area of enclosed region =20 unit2

Q: The total cost (in hundreds of dollars) to produce x units of perfume is C(x) = 3x-8 2x+9 (a) Find…

A: Given, C(x)=3x-82x+9

Q: Find the directional derivative of f(x,y)=sin(xy) at the point P0(sqrt(π),sqrt(π)) in the direction…

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Q: 2y+9x² find all -2x-1' coordinate points on the curve where X x = -1 and the line tangent to the…

A: solution is given below.. one point lie on curve at which slope of tangent line is 1.

Q: . y = sec(x)√1+cot² x csc³(x)

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Q: 5 3. Consider the sequence defined by an (a) Is this sequence monotonic? Explain. (b) Is this…

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Q: The volume V of an ideal gas varies directly with the temperature T and inversely with the pressure…

A: The pressure is =24.774 atmospheres

Q: 1. g(x)=3 tan¹ 3x 2. y=xsin ¹2x+cot ¹ √ 3. f(x) = sin ¹

A: Let's find derivative of given function.

Q: Use an appropriate substitution to solve the equation Observe that, if n = 0 or 1, the Bernoulli…

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Q: Use Implicit Differentiation to find f'(1/4) at (1/4 , 1/4) where y=f(x) and sin^2 (pix) +…

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Q: Find the differential of the function z=e-xcos(y) dz=___________________

A: Here we can see that z is function of x and y z=fx,y So, here the derivative of z is also known as…

Q: •ffe -32²-3y² dA; R= {(x, y)\x² + y² ≤ 4, x ≤ 0,y>0} R 4. (Section 16.3) Evaluate

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Q: Find an equation of the tangent plane to the given surface at the specified point. z = 2x2 + y2 −…

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Q: Rewrite in the form -8x³ - 6x²-3x+7 2x - 1 Question Help: Message instructor Submit Question -8x3 -…

A: Topic:- algebra

Q: Exercises 1-4 refer to the functions whose graphs are given in Fig. 17. 1. Which functions have a…

A: Given the graph of the functions

Q: . Let f(x) = (x² − 3)ex. Find all intervals where f'(x) is positive and all intervals where it is…

A: Please see the below picture for detailed solution.

Q: An airplane is flying at an elevation of 6000 feet directly above a straight highway. Two motorists…

A: I am attaching image so that you understand each and every step.

Q: IV. Given the functions f(x) = 2x+5, g(x)=x² - 6x +7, and h(x): = the following. Show complete…

A: Given, f(x)=2x+5, g(x)=-x2-6x+7, h(x)=3-6xx-4

Q: function

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Q: An isosceles triangle has an area of 100in^2, and the angle between the two equal sides is pie/6.…

A: Solution is done in step 2

Q: A company introduces a new product for which the number of units sold S is given by the equation…

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Q: Each of the graphs of the functions in Exercises 17-24 has one relative maximum and one relative…

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Q: 2) Form a differential equation by eliminating the arbitrary constant a and b from the equation y =…

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Q: 3 a. Find an equation for the line perpendicular to the tangent to the curve y = x - 16x + 4 at the…

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Q: We have an unknown function f(x) which satisfies    f''(x) + f'(x) -2f(x) = x2 The first term is the…

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Q: 19. Let S be the solid obtained by rotating the region shown in the figure about the (Assume a = 6…

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Q: 92. A cylindrical gasoline tank is placed so that the axis of the cylinder is horizontal. Find the…

A: It is given that, Diameter = 2 feetRadius = 1 ftρ=42 pounds/ft3

Q: Let C be the curve of intersection of the spheres x² + y² + z² = 27 and (x − 2)² + (y − 2)² + z² =…

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Q: 8. y varies jointly as x and z and inversely as the product of w and p, and y = 3/28 when x = 3,z =…

A: NOTE: Refresh your page if you can't see any equations. . y varies jointly as x and z and inversely…

Q: +6. Consider the function f(x) = 3x + Enter the number of critical points/numbers of f(x). 2…

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