Question: (a) Write expressions for the partial derivatives f x (a, b) and f y (a, b) as limits. (b) How do you interpret f x

(a) Write expressions for the partial derivatives f_x(a, b) and f_y(a, b) as limits.
(b) How do you interpret f_x(a, b) and f_y(a, b) geometrically?
How do you interpret them as rates of change?
(c) If f (x, y) is given by a formula, how do you calculate f_x and f_y?

Step by Step Solution

★★★★★

3.46 Rating (159 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Precalculus Questions!

If f (x, y) = 2x2 - 5y2, find fx and fy.

Find expressions for the partial derivatives of the following functions: a. f(x,y) = f (g(x)k(y), g(x) + h(y) b. f(x,y,z) = f(g(+ y), h(y + z)) c. f(x,y,z) = f(xy, yz, zx) d. f(x,y) = f(x,g(x),...

If f (x, y) = x 4 y 5 x 2 + y 2 write down expressions for the first-order partial derivatives, f x and f y . Hence evaluate f x (1, 0) and f y (1, 1).

Let f(x,y ) = (x+y 2 ) / (x-y 2 ) (a) Find the domain of f . (b) The level curves for f(x,y) = c, when c 1, are conic sections. Identify the type. Also, identify the level curve when c = 1. (c)...

Question 3 (20 marks) The following regressions were run using 2,108 observations on females living in the US. The respondents in the sample are aged between 27 and 31, with many working and raising...

function = explicit(mx) %% Problem Number: 49 L = 45; tmax = 80; U = 0.8; D = 1.2; Xs = 4; Cs = 10; XFlux = 36; % % % % % % % m s m/s m2/s m kg/m m % Calculating dx and dt based of mx input dx =...

CS 7641 CSE/ISYE 6740 Homework 3 Le Song Deadline: 11/07 Mon, 11:55pm Submit your answers as an electronic copy on T-square. No unapproved extension of deadline is allowed. Zero credit will be...

Further Exercises 7.4 . The Earth is round. but in everyday life, we get along ne acting as though it were flat. Why is this possible? . Compute the following partial derivatives: f l. f(X. Y) = X3...

Can you provide the responses for below with explanation and R code. A data set (Xi, yi), for i = 1, ...,50, is available in "HW11 data_1.csv" for the logistic regression model; exiBj P(Y: = j | B,...

1. (24 points) Consider consumer happiness given by the function V = u(x1, x2, . . . , xN) where xi is the quantity of good i consumed. a) (1 point) How many first order partial derivatives does u...

What are financial ratios and why are they useful?

The accompanying data on milk volume (in grams per day) were taken from the paper Smoking During Pregnancy and Lactation and Its Effects on Breast Milk Volume (American Journal of Clinical Nutrition...

A recent Gallup poll found that of 800 randomly selected drivers surveyed, 70% thought that they were better-thanaverage drivers. It is reasonable to define average so that in the population, at most...

Why do the AIDA model and similar approaches need to be modified when writing persuasive messages in social media? [LO-3]

The population in Exercise 53 for 0 t 100. Mark where the population has gone down by half. Plot semi log graphs of the values.

The antler size A(t) in centimeters of an elk increases with age t in years according to A(t) = 53.2e0.17t and its shoulder height L(t) increases according to L(t) = 88.5e0.1t. The following pairs of...

Suppose a population of viruses in an infected person grows according to V(t) = 2.0e2.0t and that the immune response (described by the number of antibodies) increases according to I(t) = 0.01e3.0t...

Make the financial ratios analysis of MyDeco Corporation Financial Statements & Stock Price: MyDeco Corp. (66.7) (All data as of fiscal year end; in $ million) 2009 2010 2011 2012 2013 404.3 363.8...

written work please not excel Question 13 (14 points) Best Ever Results Inc. has a project under consideration with the following estimated cash flows: An initial investment of $420,000. A return of...

Ross White's machine shop uses 2,500 brackets during the course of a year, and this usage is relatively constant throughtout the year. These brackets are purchased from a supplier 100 miles away for...