Answered: Show mathematically that MRS is…

Math

Calculus

Show mathematically that MRS is increasing for U=1-ex +e2y and is diminishing for U=lnX +LnY

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter3: The Derivative

Section3.3: Rates Of Change

Problem 30E: If the instantaneous rate of change of f(x) with respect to x is positive when x=1, is f increasing...

See similar textbooks

Related questions

Q: 3x What is f'(x) given the integral function f(x) = (4u – 2) du? O f'(x) = 4x-2 %3D O f'(x) = 12x -2...

Q: Solve the components of the given equation of conic sections and sketch the graph: a. x2 + y2 – 10x ...

A: Given

Q: 2. Divide the class into groups of 10. Measure the height of each member. Find the sampling distribu...

Q: 5 on the interval [-4,4] x3 Find the average rate of change of g(x) = 3x2 +

A: Given problem:-

Q: II. Determine the derivative of the ff. logarithmic functions 4. y = 8 log , 7x² 5. y = - 5 log , (1...

A: As per our guideline we solve only first three parts

Q: Determine whether the series converges, and if so find its sum. Enter the exact answer as an imprope...

Q: Use any method to determine whether the series converges or diverges. (k!)° (9k)! O The series diver...

Q: x'- 36 lim 16 x+6 (a) Vx+11-4 lim- (b) х -5 (c) lim- +2 2-x

A: Since the student has posted many sub-parts of the question and does not mention any specific part, ...

Q: When is an equation considered as a solution of differential equation?

Q: Find the nth Taylor polynomial for the function, centered at c. f(x) = In(x), n = 4, c = 5 P4(x) =

Q: 1. Write a differential equation that models the given situation. The stated rate of change is with ...

A: let P denote pressure of a gas T is temperature of gas V is volume of gas

Q: y considering different paths of approach, show that the function below has no limit as (x,y)→(0,0)....

Q: sing u-substitution, the integral Jf(x)dx reduces to a new integral J glu) du. If g(u) = , evaluate ...

A: Topic:- application of integration

Q: dx (x² + 9)² 5.

Q: Question 16 3 In?x + 1 Evaluate x (In3x + In x) 1 In lin³x + In x| + C A +x, B In in?x + 1| + C © 3I...

Q: Find the nth Taylor polynomial for the function, centered at c. 1. f(x) n = 4, c = 3

Q: 3. Find all values of a, b, c so that the following function is continuous for all values of x x-1 s...

A: Please see the below picture for detailed solution.

Q: Find the constants xo, X1, and c so that the quadrature formula 1 dx = 5 (xo) +c1 f (x1) f (x) has t...

A: We have to find the constants x0, x1, and c1 so that the quadratic formula ...

Q: Express the repeating decimal as a fraction. 0.904818181818... 0.904818181818... =

A: topic - rational numbers

Q: Pinocchio’s nose length y (in inches) is dependent on his lie count (s). Geppetto has modeled this ...

A: Given equation, yy=as where, y is Pinocchio’s nose length (in inches) s is his lie count a is a magi...

Q: Suppose f(x) = "6r V1+f dt.

A: Topic = Integration

Q: formula

Q: 22. Given the function f at the following values, 1.8 2.0 2.2 2.4 2.6 f(x) 3.12014 4.42569 6.04241 8...

A: Definite integration problem

Q: show that for positive epsilon, |x-4| |3x-12|<e

A: a⇔b implies if a holds then also b holds and vice versa.

Q: Market research for a certain ice cream company indicates that if the price per cup of ice cream is ...

A: Given that for a certain ice cream company indicates that if the price per cup of ice cream is $50.0...

Q: Use synthetic division to determine whether x - c is a factor of the given polynomial. x3 - 11x2 + 3...

A: By using the synthetic division to determine we have to check whether x-c is a factor of the given p...

Q: (a) With the use of a suitable limit, find the first differential of Vr² +b² with respect to r i.e. ...

A: topic - derivative using first principle

Q: Evaluate the integral using tabular integration by parts. 4 x° V2 x + 1 dx +C

Q: Show whether the following series converges 1 1 1 +. 82 1 22 52 (Зп — 1)° using the comparison test.

Q: (*y3 - ) + y² = 0 1 1+9r

Q: Find the distance between the points (distance formula) 3.(-1, 1/2), (3/4, -4) 4.(a, b), (c, 0)

Q: Describe the transformations in each graph. Sketch the graphs of the following functions by hand, us...

A: a) The given function is: f(x)=-2 cos 3x-π3+12

Q: d) If the coefficients are rounded off of - 0.31x + 2.73 find the absolute and relative in y x + 0.3...

A: Find absolute and relative in y

Q: Find the average rate of change of f(x) = 9x² – 6 on the interval [5, t]. Your answer will be an exp...

Q: Use the definition of Taylor series to find the Taylor series (centered at c) for the function. f(x)...

Q: 4. y = 2 -10x 5. y = 88 8x + 888 6. y = 2021 7×^6

A: According to our company's guidelines I can only answer first three subparts of the question since y...

Q: xp xy6x -x

A: The given integral ∫1x6x-x2dxThe integral formula,117. ∫duu2au-u2=-2au-u2au+C

Q: Using Figure 1, complete the following function. V u Figure 1 sing = %3D u/r v/r ^yn O r/v v/u r/u O...

A: Given problem:-

Q: 1 Find 는 dx by using chain rule, if f = u + u = T x , at x = = 4 cos?u

Q: 3. Evalnate. the. following.double.intagrals.by.comverting to Polar.Caa.r.dinates. 2 2 Anse. T(e-1) ...

Q: At least one of the answers above is NOT correct. Match each of the following with the correct state...

A: This is question related to series and sum calculation. Based on several method available for testin...

Q: Direction: Provide what is asked in each item. 1. For what value of a does the limit of the piecewis...

A: Note: According to our expert guidelines only first three subparts are to be answered kindly repost ...

Q: Find the nth Maclaurin polynomial for the function. f(x) = e¯X, n = 5 Ps(x) = %3D MastarIt

A: Given

Q: Express the arc length of the curve y =+ between x= -3 and x = -1 as an integral. A dx. E) None of t...

Q: 2. f(x) = Va +æ + 1

A: Here, the given function is: f(x)=x2+x+13 Now, f'(x)=13(x2+x+1)13-1(2x+1) =13(x2+x+1)-23(2x+1...

Q: The base of a solid sitting on the ry-plane is the region enclosed by the curves y = c* , y= e$ and ...

Q: Use the binomial series to find the Maclaurin series for the function. f(x) (1 + x) %3D f(x) = Σ n =...

A: Maclaurin series is nothing but taylor series expansion at a=0 point. First we will find the maclaur...

Q: The equivalent Cartesian equation of the polar equation r = tan0sec0 is: A) y = x. B) y= x2. C) ху —...

Q: Find the distance between the points (distance formula) 5.(2a+c, 2d), (2b-c, 2c) 1.(3, 2), (4, -3)

Q: f(x) = x(6 – x)-

A: Given :f(x)=xa(6-x)b 0≤x≤6

Question

Show mathematically that MRS is increasing for U=1-e^x +e^2y and is diminishing for U=lnX +LnY

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps with 3 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

Find the average rates of change of f(x)=x2+2x (a) from x1=3 to x2=2 and (b) from x1=2 to x2=0.
If the instantaneous rate of change of f(x) with respect to x is positive when x=1, is f increasing or decreasing there ?
Determine whether each of the following statements is true or false, and explain why. The chain rule is used to take the derivative of a product of functions.
Determine whether each of the following statements is true or false, and explain why. The derivative of a sum is the sum of the derivatives.