1. (Section 15.8) The function f(x, y) = z²y has an absolute maximum and absolute minimum subject to constraint x² + y² = 1. Use Lagrange multipliers to find these values.

Q: Refer to the given figure. Write the radius r of the circle in terms of a and 0.

A: Given diagram:- Here,  θ=Angle

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: Write an equation for each line. 15. through (2, 2), y-intercept 10

A: since you have posted multiple questions i can do first question as per our company guidellines.…

Q: 1. Separation of variables/ a. xy³ dx + (y + 1)e-*dy = 0

A: Here we have to solve the given differential equation

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

A:

Q: Evaluate f(x) ƒ(1) = f(x + 7) = f(x) + f(7) f(x + h) = = = x + 2 at the indicated values.

A:

Q: Example 4 (Calculator Active): For 0 ≤s ≤ 5000, the total amount a local college spends on printing…

A: NOTE: Refresh your page if you can't see any equations. . the given cost function is  where…

Q: Let F(x)=f(f(x))=f(f(x)) and G(x)= (F(x))2 and suppose that f(6)=7, f(7)=2, f′(7)=3 ,f′(6)=8 Find…

A: As we know that for composition of function F(x)=ff(x), F'(x)=f'f(x)×f'(x)

Q: Find the particular solution of each of the following. (4+sine)y'=e*(6soc² e* - ycose); y(ln x) =…

A:

Q: Find Vz. = = sin(4y² - 6xy) NOTE: Give your answer in unit vector notation; that is, in terms of i…

A: Given; z=Sin(4y2-6xy)

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: Devise an exponential decay function that fits the given data, then answer the accompanying…

A: Here, the equation used is: P=P0ekt...(1) where P is the pressure of the atmosphere at t=0 and k is…

Q: The formula for nCr has the same numerator as the formula for nPr but contains an extra…

A: The NCR formula is used to calculate the number of possible combinations in which r objects are…

Q: (a) Find the distance from P1 = 1 - 2, - 32 to P2 = 13, - 52.(b) What is the midpoint of the line…

A: Given, P1=-2, -3 and P2=3, -5

Q: Determine whether or not the following equation is exact: 3 dy xy + (²x² + 2y² − 20) = 0, y(0)=1. dx…

A: See this solution in below

Q: Given the following functions: f(u)=u^5/2 and g(x)=x^6+1. Find f(g(x))= f′(u)= f′(g(x))= g′(x)=…

A:

Q: f(x)=(2x+1)^4   Find the values of x where the tangent line is horizontal Values of X= ___

A:

Q: Use a software program or graphing utility to solve the system of linear equations. (If there is no…

A:

Q: 3. Determine whether the sequence an = n cos ní is bounded, bounded above. bounded belew, or none of…

A:

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: Express the function h(x) = 5log(x² + 6) the form fog. If f(x) = 5log(x), find the function g(x)

A: We can find the function g(x) from the given composite function in the below steps.

Q: A certain drug is eliminated from the bloodstream with a half-life of 34 hours. Suppose that a…

A: Given half life of 34 hours Initial does of 75 mg

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

A:

Q: Calculate the slope of the line that passes through (-11, -6) and (1, -4). O - 1 O -16 1 O 6

A:

Q: Find the limit of each of the following sequences, using L'Hopital's rule when appropriate. √n Vn+1

A:

Q: 3. Consider the initial value problem y′ +y=1-², y(0) = 30› where yo denotes some real constant. (a)…

A: To find the solution of given differential equation.

Q: (Question-Solution-Final Answer-Conclusion format) B. Generate differential equation by elimination…

A:

Q: determine whether the given function is linear or nonlinear. If it is linear, determine the equation…

A: Note:- We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: Use the Fundamental Counting Principle to solve:You are taking a multiple-choice test that has five…

A: Given data:- n = number of questions = 5 Number of choices for each question = 3 We have to find a…

Q: - A) -16x-5-x-2/3 C) 3 4) Find: d 4 dx x4 5 -4/3 B) ਪ੍ਰੈਲ-5-1582/3 D) - 1 5-2/3 433 3

A:

Q: a. Distribute b. Solve { ª²³ (a²³ + 2a ²).

A:

Q: Please have a systematic way of solution (Question-Solution-Final Answer-Conclusion format) E.…

A: Question: Please have a systematic way of solnerate solution of the first-order differential…

Q: If sin(0) = 3 - and is in quadrant II, then find the EXACT value of sec(0). "

A: Given that sinθ=35 Use, the formula sinθ= PH Where P is the perpendicular and H is the hypotenuse.…

Q: Constructing an Open Box An open box with a square baseis required to have a volume of 10 cubic…

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

Q: Evaluate the following integral using trigonometric substitution. S dx (x²-36) 3/2 " X>6

A:

Q: List the intercepts and test for symmetry: y2 = x + 4

A: Given data:- The given equation,y2 =x+4

Q: 7. 1 (x) == x¹- -2x³ + x-10. Find the hypercritical value(s) of f(x)=

A:

Q: 5. Bernoulli's Equations a. 6y²dx-x(2x³ + y)dy = 0

A:

Q: Sketch the region bounded by the curve x 2 = y and the line x = volume of the solid generated by…

A: solution:-the region bounded by y=x2-2 & x=y+2revolving around y=1

Q: Find the directional derivative of f(x, y, z) = yz + x¹, at (3, 2, 1) in the direction of = + + k 7…

A: Given Find gradient

Q: If f1x2 = x2 - 4, find f1 - 22.

A: Given, fx=x2-4

Q: Select all of the following graphs which are one-to-one functions. 0 0 Ay 1-4 -3 A -2 -3 -5 -4 -3 -2…

A:

Q: A B C D lim /(x) = 0 x+2+ lim f(x) = 2 x →-2+ lim /(x) = 0 x+2- lim f(x) = -3 x--2 -5-4-3-2-1 Y -3-…

A: Find limit of function

Q: You are dealt one card from a standard 52-card deck. Find the probability of being dealt a heart.

A: Given: Total number of cards = 52 Formula used: Probability = Number of favourableNumber of outcome

Q: Evaluate the following integral. S= 2 x³√x² - 1 dx =

A:

Q: Evaluate the limit If the limit does not exist enter DNE. Limit Number = lim x 6 x2 x-6 6 x

A: To evaluate the following limit.If the limit does not exist then to enter DNE.limx→6 x-6x2-6x

Q: 9. Determine the convergence of the following series using the ratio test. If the ration test is…

A: Ratio Test

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

A:

Q: 4. Consider the initial value problem y = x+y, y(0) = 1. (a) Use Euler's method with h = 0.1 to…

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

Q: The indicated function y₁(x) is a solution of the given differential equation. Use reduction of…

A: