Consider the ellipsoid x² + y² + 3z² = 8. Find all the points where the tangent plane to this ellipsoid is parallel to the plane 2x − y + 3z = 0. (If there are several points, separate them by commas.)

Q: Another model for a growth function for a limited population is given by the Gompertz function,…

A: The givne growth function for the limited population is dpdt=clnkpp…

Q: Find the directional derivative of f at P in the direction of a. f(x, y) = 13 tan (²); P(-14,14);…

A: The given function is fx,y=13tan-1yx. To find the directional derivative, find the gradient of f.…

Q: Evaluate the following integral. 9 4 dx 1-√√x

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Q: Find the equation of the tangent line to the graph of f(x) = √x + 100 at the point (0, 10).

A: Given query is to find the equation of the tangent.

Q: -6 (-3,1) -5 86°F Sunny I 1 -4/ -3 -2 1 / -1 4 3 2 - 0 -1 -2 -3 -4 -5 -6 2 W Use the graph to…

A: Given query is to find the slope of the tangent line.

Q: A mathematical model for the average of a group of people learning to type is given by N(1) (2 hours…

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Q: (c) Let y = (In x)2. Compute y' by using logarithmic differentiation.

A: The given function y=ln x2x We have to find the derivative of y using logarithm differentiation.

Q: (6) ft sin 2t dt.

A: We need to find out the integration.

Q: If ƒ(1) = 5, must lim x approaches 1 ƒ(x) exist? If it does, then must lim x approaches 1 ƒ(x) = 5?…

A: Given :-f(1)=5Now, we have to find that limx→1f(x) exists or not.And if  limx→1f(x) exists then…

Q: 6 5 4 3 2 I 1 it y = f(x) X

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Q: SIT lim t-0 CATA 3+t-√3-t t anot

A: To find the limit.

Q: 1) Using the definition, calculate the derivatives of the functions. Then find the values of the…

A: Solve by derivatives

Q: find the average rate of change from 2 to 3 for each function f. Be sure to simplify.   f1x2 = 3x -…

A: The average rate of change of function denotes how much the function changed per unit over the given…

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Q: Solve the following equations. Leave answer in exact form. 1. e³x = 5 2.5e-7 = 8

A: Given, e3x=5Taking ln on both sideln(e3x)=ln(5)We know that ln(ab)=bln(a)3xln(e)=ln(5)We know that…

Q: True or False The slope of a nonvertical line is the averagerate of change of the linear function.

A: The average rate of change of the linear function is the slope of a nonvertical line.

Q: the cable of a suspension bridge hangs in the form of a parabola. the distance between two towers is…

A:

Q: In problems 14-16, use the properties of definite integrals to support your answer. Be specific.…

A: Given, ∫26f(x)dx=9⇒f(6)-f(2)=9…

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Q: Draw the unit circle and then shade in an arc of the circle's boundary with a shaded arc length of…

A: Length of arc, l = r * theta  Where, r = Radius of circle       theta = Angle subtended by arc at…

Q: Graph the functions ƒ(x) = sqrt(x )and g(x) = sqrt(1 - x) together with their (a) sum, (b) product,…

A: Given data:- The given functions is, fx=xgx=1-x

Q: A chemical substance has a decay rate of 6.5% per day. The rate of change of an amount N of the…

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Q: 4) Thomas kicks a rugby ball from 0.8m above ground in Devon's direction. The ball follows a…

A: Vertex form of parabola:- y=a(x-h)2+k  Here vertex(h, k)  When a>0 then parabola opens up and…

Q: Compute the directional derivative of the following function at the given point P in the direction…

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Q: Find the given limit (x² - 1)(y² - 4) lim (x,y) →(1,2) (x - 1)(y-2)

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Q: fxe* dx.

A:

Q: A cross section of the parabolic mirror in a car headlight is y² = 32x. Where should the bulb be…

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Q: (g) Differentiate g(x) = /1-². cos¹ (√) 3

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Q: Expand:

A: Given data, log7x549y10

Q: graph each equation.   y = 2x

A: Given data:- The given equation is, y=2x

Q: Similarly, approaching along the y-axis yields a limit equal to 0. Since these two limits are the…

A: Given that a limit problem and we solve this problem by using general property of limit.   Here i…

Q: Find an equation for the plane containing the two (parallel) lines v1 = (0, 1, −3) + t(8, 2, −1) and…

A: Find an equation for the plane containing the two (parallel) lines  v1 = (0, 1, −3) + t(8, 2, −1)…

Q: An offshore oil well is 5 kilometers off the coast. The refinery is 4 kilometers down the coast (see…

A: Solution

Q: If the slope m of the graph of a linear function is ,the function is increasing over its domain.

A: If the slope m of the graph of a linear function is _______, the function is increasing over its…

Q: In Exercises 1–6, find the domain and range of each function.1. ƒ(x) = 1 + x2     2. ƒ(x) = 1 - 2x3.…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: Use the Lagrange multipliers to find the maximum and minimum values of f(x, y) = 2x + y - 2z subject…

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Q: A wooden beam has a rectangular cross section of height h and width w (see figure). The strength S…

A: Given :d=46 cm

Q: Integrate [8³e³ 13 ft³e est dt t³ est dt. =

A: The solution to find the integral  of given integration is as follow.

Q: If bn = determine whether this sequence converges or 271 Convergent, give the limit of this…

A: we know that sequence is defined as the set of natural numbers N and X any set, then a function…

Q: (b) Let y = (2x + 1) cos. Compute by using logarithmi dy dx

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Q: If y=f(x)=7e^x + 3x^4 - 20x - 5, Find the equation of the

A: Using derivative first find slope m,

Q: 7. Use the integral test to determine the convergence of the following series: ∞ n=2 n ln n น

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Q: Write a word problem that can be solved by evaluating 7P3.

A: Given: 7P3. Formula Used: Prn = n!(n-r)!

Q: Integrate the following. 6° 0 8x 12e dx =

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Q: y=5(x^(2)+3)^(5)+9(x^(2)-1)^(2x) then (dy)/(dx)

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Q: Exercises  tell how many units and in what directions the graphsof the given equations are to be…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: Use the Fundamental Counting Principle to solve:A television programmer is arranging the order that…

A: Fundamental Counting Principle:- The fundamental counting principle is a rule used to count the…

Q: FIND F'(x) F(x) = 2 tanx 1+cosx

A: To differentiate the given function.

Q: Evaluate the following integral using trigonometric substitution. x² 441-x² S dx

A: ∫x2441-x2dx

Q: Find a unit vector in the direction in which f(x, y) = 8 cos(3x − 5y) ㅠ P(20), and find the rate of…

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