Using Lagrange multipliers, find the maximum and minimum values of the function f(x, y, z) = 8x - 9z subject to the constraint x² + 5y² + z² − 4 = 0. Location of maximum (enter as coordinates (x,y,z)): Maximum value: Location of minimum (enter as coordinates (x,y,z)): Minimum value:

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

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Q: Assume the acceleration of the object is a(t) = -32 feet per second per second. (Neglect air…

A: topic:- calculus

Q: |-2 Evaluate the triple integral ²³ cos (y²) dz dx dy.

A: Here we have to perform triple integration

Q: Compute the directional derivative of the function g(x,y) = sin((5x - 4y)) at the point P(3,3) in…

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Q: 5. Find the divergence and curl of the vector field F(x, y, z) = (xy - 2², 2x+cos(yz), 2y² - sinz)…

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Q: Use the estimate |RN| ≤ b + 1 to find a value of N that guarantees that the sum of the first N terms…

A: Using the concept   RN≤bN+1 to find the value of N terms of the following series.          For  bn…

Q: Given that logp q = x 2 and logq p = 1 2x−1 , find x

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Q: Suppose an object is moving along a verticals line. It’s vertical position is L(t)= -t^2 -4t+12.…

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Q: The series k=1 5( − 1)k+1 - kl.1 O converges diverges.

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Q: The hypotenuse of right triangle is 74 meters long. The difference between the other two sides is 46…

A: We know that for a right triangle , Let hypotenuse is c and other two sides are a and b. Then…

Q: Find an equation or inequality that describes the following object. A sphere with center (4,1,1) and…

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Q: y = 16 X + x² at x at x = 4.

A: Given Equation :- y=16x+x2  Find the equation for the tangent line to the curve at x=4

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: i) Find the exact length of the curve y X y = 2 X + — ii) Find the exact area of the surface…

A: Let's find exact length and area of surface.

Q: Find the limit. Ilm x4 1 5 g B

A: using limit, direct putting value since denominator is polynomial

Q: II) Let f be the piecewise function f(x) = x³ + 6x² + 8x x+2 1-x-2, -, x≤-1, x -2 -1 1 1) Sketch the…

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Q: Refer to the figure and find the volume generated by rotating the given region about the specified…

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Q: sporting goods store sells 64 tennis rackets per month at $90$ each. The owners estimate that for…

A: Given the query is to find the price to maximize the revenue.

Q: Lotteries In a New York State daily lottery game, a sequence of four digits (not necessarily…

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Q: Find a power series representation for the function. f(x) = x4 tan-1(x³) Σ( n=0 f(x) = Determine the…

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Q: 16. Use properties of logarithms to expand log (²₁¹). t14

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Q: Identify the type of conic section whose equation is given. 2x2 = y2 + 2 parabola ellipse…

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Q: Air traffic controllers continuously monitor the angles of elevation and to an airplane from the…

A: Concept: The angle of elevation: The angle of elevation is the angle created between the line of…

Q: If the revenue function for a particular commodity is R(p) = q(p) = Give a reason for your answer. R…

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Q: Question 1 options:   A vector has initial point (-5, 8) and terminal point (0, 2). Write the…

A: let initial point A (-5,8)=(x1,y1) terminal point B(0,2)=(x2,y2)

Q: y" + 3y' + 2y = U₂(t); y(0) = 0, y'(0) = 1

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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: Determine the vertical and horizontal asymptote of the graph of the function. h(x)=x-2/2x2+8x+8

A: We can find the vertical and horizontal asymptotes as below.

Q: Which one is correct for the sum of the geometric series O O O 9 10 11 5 17 10 6 5 O Divergent Σ1…

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Q: The cost function for a particular product is given by C(x)=0.001x^3 −0.24x^2 +27.9x +110 dollars,…

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Q: Identify the vertical and horizontal asymptotes of f(x) = 2x+1 X-4 vertical: x = horizontal: y…

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Q: f(x) = 5* g(x) = log5 (²²= 4) Find (fog)(x) and obtain its domain. h(x): - 6 <- x 2x-5

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Q: ขน lim (x,y) → (0,0) x² +10y²

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Q: Identify the function represented by this graph. -5 -4 -3 -2 -1 5 4 3 2 -3 ✔ 1 2 3 4 5 x

A: Topic = Functions

Q: The interest rate for a savings fund was 3.80% compounded semi-annualy for the first 4 years and…

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Q: Find the divergence and curl of the vector field F(x, y, z) = (xy — 2², 2x+cos(yz), 2y² - sinz) at…

A: Here we have to find the divergence and curl of given vector field.

Q: Find the marginal profit function if cost and revenue are given by C(x)= 185 +0.3x and R(x) = 3x…

A: Recall: Profit, P(x)=Revenue-Cost Marginal profit=P'(x) We have, R(x)=3x-0.02x2, C(x)=185+0.3x

Q: Revenue The Better Baby Buggy Co. has just come out with a new model, the Turbo. The market research…

A: Given ,  The Better Baby Buggy Co. has just come out with a new model, the Turbo The market research…

Q: Sketch the graph of f ( x ) = 2x³ - 3x² + 3 , indicating the points of inflection and the intervals…

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Q: 9 outside cardioid r = 1 + cos 0 inside circle r = 3 cos ( 10 lemniscate ² = 4 cos 20 outside r = =…

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Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. =x²+²x≤x≤1 3x 2…

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Q: The integrating factor of the given DE are already given below. What is the value of “n” ?…

A: We need to find n.

Q: Calculate Rs for f(x) = 4x² + 8x over [-1, 1]. (Give an exact answer. Use symbolic notation and…

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Q: Let a-2-3j.kb-41-) and c-1-31-2k. If d is such that da-9. db-7 and dc-6, then d is equal to 01-31-2…

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Q: Use an appropriate Taylor series to find the first four nonzero terms of an infinite series that is…

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Q: equation

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Q: Find the exact sum of the following series 0 In ( ) 3 5 OH(-) - 12 (²³) In 3 (²/²) - ²3/ In 23 ○ In…

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Q: How/why does f(x)=10/x become f(x)=10/x^2?

A: The process of how f(x)=1x become f'(x)=-10x2 has been explained in next step.

Q: i) Find the general term (an) of the sequence 3e-¹, 10e-2, 29e-³, 66e-4, 127e-5,218e-6, ... ii)…

A: The given sequence is;  3e-1, 10e-2, 29e-3, 66e-4, 127e-5, 218e-6, ...

Q: b) Find the volume of the solid obtained by rotating the region bounded by the curve y = -x² + 11…

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