New Semester
Started
Get
50% OFF
Study Help!
--h --m --s
Claim Now
Question Answers
Textbooks
Find textbooks, questions and answers
Oops, something went wrong!
Change your search query and then try again
S
Books
FREE
Study Help
Expert Questions
Accounting
General Management
Mathematics
Finance
Organizational Behaviour
Law
Physics
Operating System
Management Leadership
Sociology
Programming
Marketing
Database
Computer Network
Economics
Textbooks Solutions
Accounting
Managerial Accounting
Management Leadership
Cost Accounting
Statistics
Business Law
Corporate Finance
Finance
Economics
Auditing
Tutors
Online Tutors
Find a Tutor
Hire a Tutor
Become a Tutor
AI Tutor
AI Study Planner
NEW
Sell Books
Search
Search
Sign In
Register
study help
mathematics
calculus 4th
Calculus 4th Edition Jon Rogawski, Colin Adams, Robert Franzosa - Solutions
Use the Linear Approximation to show that if I = xayb, then 1 za- - y + b y
The monthly payment for a home loan is given by a function ƒ(P, r, N), where P is the principal (initial size of the loan), r the interest rate, and N the length of the loan in months. Interest rates are expressed as a decimal: A 6% interest rate is denoted by r = 0.06. If P = $100,000, r = 0.06,
Automobile traffic passes a point P on a road of width w feet at an average rate of R vehicles per second.Although the arrival of automobiles is irregular, traffic engineers have found that the average waiting time T until there is a gap in traffic of at least t seconds is approximately T = teRt
The volume V of a right-circular cylinder is computed using the values 3.5 m for diameter and 6.2 m for height. Use the Linear Approximation to estimate the maximum error in V if each of these values has a possible error of at most 5%. Recall that V = πr2h.
Show that if ƒ(x, y) is differentiable at (a, b), then the function of one variable ƒ(x, b) is differentiable at x = a. Use this to prove that ƒ(x, y) = √x2 + y2 is not differentiable at (0, 0).
This exercise shows directly (without using Theorem 1) that the function ƒ(x, y) = 5x + 4y2 from Example 1 is differentiable at (a, b) = (2, 1). THEOREM 1 Confirming Differentiability If fx(x, y) and fy(x, y) exist and are con- tinuous on an open disk D, then f(x, y) is differentiable on D.
Show directly, as in Exercise 43, that ƒ(x, y) = xy2 is differentiable at (0, 2).Data From Exercise 43This exercise shows directly (without using Theorem 1) that the function ƒ(x, y) = 5x + 4y2 from Example 1 is differentiable at (a, b) = (2, 1). THEOREM 1 Confirming Differentiability If fx(x, y)
Use the definition of differentiability to prove that if is differentiable at (a, b), then ƒ is continuous at (a, b).
Let ƒ(x) be a function of one variable defined near x = a. Given a number M, set e(x) = f(x) - L(x) e(x) L(x) = f(a) + M(x a), Thus, f(x)=L(x) + e(x). We say that f is differentiable at x =a if M can be chosen so that lim xa |xa| (a) Show that if f(x) is differentiable at x = a, then f(x) is
Define g(x, y) = 2xy(x + y)/(x2 + y2) for (x, y) ≠ 0 and g(0, 0) = 0. In this exercise, we show that g(x, y) is continuous at (0, 0) and that gx(0, 0) and gy(0, 0) exist, but g(x, y) is not differentiable at (0, 0). (a) Show using polar coordinates that g(x, y) is continuous at (0, 0). (b) Use
Match graphs (A) and (B) in Figure 18 with the functions: (i) f(x, y) = -x + y (ii) g(x, y) = x + y
Match each of graphs (A) and (B) in Figure 19 with one of the following functions: (i) f(x, y) = (cos x) (cos y) (ii) g(x, y) = cos(x + y)
Match the functions (a)–(f) with their graphs (A)–(F) in Figure 20. (a) f(x, y) = (b) f(x, y) = (c) f(x, y) = (d) f(x, y) = (e) f(x, y) = x + [y] cos(x - y) -1 1+9x + y cos(y2)e-0.1(x + y) -1 1 + 9x +9y (f) f(x, y) = cos(x + y)e-0.1(x + y)
Match the functions (a)–(d) with their contour maps (A)–(D) in Figure 21. (a) f(x, y) = 3x + 4y (c) h(x, y) = 4x - 3y (b) g(x,y)=x-y (d) K(x,y)= x - y
Sketch the graph and draw several vertical and horizontal traces. f(x, y) = 12-3x - 4y
Sketch the graph and draw several vertical and horizontal traces. f(x, y) = 12-3x - 4y
Sketch the graph and draw several vertical and horizontal traces. f(x, y) = x + 4y
Sketch the graph and draw several vertical and horizontal traces.ƒ(x, y) = y2
Sketch the graph and draw several vertical and horizontal traces.ƒ(x, y) = sin(x − y)
Sketch the graph and draw several vertical and horizontal traces. f(x, y) = 1 x + y +1
Sketch contour maps of ƒ(x, y) = x + y with contour intervals m = 1 and 2.
Sketch contour maps of ƒ(x, y) = x + y with contour intervals m = 1 and 2.
Draw a contour map of ƒ(x, y) with an appropriate contour interval, showing at least six level curves. f(x, y) = x - y
Draw a contour map of ƒ(x, y) with an appropriate contour interval, showing at least six level curves. f(x, y) = y x
Draw a contour map of ƒ(x, y) with an appropriate contour interval, showing at least six level curves. f(x,y) = X
Draw a contour map of ƒ(x, y) with an appropriate contour interval, showing at least six level curves.ƒ(x, y) = xy
Draw a contour map of ƒ(x, y) with an appropriate contour interval, showing at least six level curves.ƒ(x, y) = x2 + 4y2
Draw a contour map of ƒ(x, y) with an appropriate contour interval, showing at least six level curves.ƒ(x, y) = x + 2y − 1
Draw a contour map of ƒ(x, y) with an appropriate contour interval, showing at least six level curves.ƒ(x, y) = x2
Draw a contour map of ƒ(x, y) with an appropriate contour interval, showing at least six level curves.ƒ(x, y) = 3x2 − y2
Find the linear function whose contour map (with contour interval m = 6) is shown in Figure 22. What is the linear function if m = 3 (and the curve labeled c = 6 is relabeled c = 3)? -6 -3 y 3 + x 6 c=6 c=0
Use the contour map in Figure 23 to calculate the average rate of change:(a) From A to B. (b) From A to C. B -6 -4 -2 y A 2 4 C c=-3 c=0 + x 6
Refer to the map in Figure 24.(a) At which of A–C is pressure increasing in the northern direction?(b) At which of A–C is pressure increasing in the westerly direction? 1024 1012 1020 1006 1024 1020 1016 1004 1028 1020 1024 (B)1016 1028 1032 1032 (A) 1004 -1000 1008 1008 1012 1012 1016 1016
Refer to the map in Figure 24.For each of A–C indicate in which of the four cardinal directions, N, S, E, or W, pressure is increasing the greatest. 1024 1012 1020 1006 1024 1020 1016 1004 1028 1020 1024 (B)1016 1028 1032 1032 (A) 1004 -1000 1008 1008 1012 1012 1016 1016 1016 1016
Refer to the map in Figure 24.Rank the following states in order from greatest change in pressure across the state to least: Arkansas, Colorado, North Dakota, Wisconsin. 1024 1012 1020 1006 1024 1020 1016 1004 1028 1020 1024 (B)1016 1028 1032 1032 (A) 1004 -1000 1008 1008 1012 1012 1016 1016 1016
Let T(x, y, z) denote temperature at each point in space. Draw level surfaces (also called isotherms) corresponding to the fixed temperatures given. T(x, y, z)= 2x + 3y -z, T = 0, 1, 2
Let T(x, y, z) denote temperature at each point in space. Draw level surfaces (also called isotherms) corresponding to the fixed temperatures given. T(x, y, z)= x-y + 2z, T = 0,1,2
Let T(x, y, z) denote temperature at each point in space. Draw level surfaces (also called isotherms) corresponding to the fixed temperatures given. T(x, y, z)= x + y -z, T = 0, 1,2
Let T(x, y, z) denote temperature at each point in space. Draw level surfaces (also called isotherms) corresponding to the fixed temperatures given. T(x,y,z) = x - y + 2, T = 0, 1, 2,-1, -2
ρ(S, T) is seawater density (kilograms per cubic meter) as a function of salinity S (parts per thousand) and temperature T (degrees Celsius). Refer to the contour map in Figure 25.Calculate the average rate of change of ρ with respect to T from B to A. Temperature T (C) 25+ 20- 15- 10- 5 1.02307
Let Using polar coordinates, prove that and that does not exist. Show that g(x, y) = cos2θ and observe that cos θ can take on any value between −1 and 1 as (x, y) → (0, 0). f(x,y) = x/(x + y) and g(x, y) = x/(x + y).
Use any method to evaluate the limit or show that it does not exist. lim (x,y)(0,0) x - y x + y
Use any method to evaluate the limit or show that it does not exist. lim (x,y) (0,0) x - y x + y
Use any method to evaluate the limit or show that it does not exist. lim (x,y) (0,0) 3x + 2y
Use any method to evaluate the limit or show that it does not exist. x4-y4 lim (x,y) (0,0) x4 + xy + y4
Show that the limit does not exist by approaching the origin along one or more of the coordinate axes. x+y+z lim 2 (x,y,z) (0,0,0) x + y + z
Show that the limit does not exist by approaching the origin along one or more of the coordinate axes. x - y+z lim (xyz) (0,0,0) x2 + y + z
Use the Squeeze Theorem to evaluateSqueeze Theorem lim (x-16) cos (x,y) (4,0) 1 (x-4) + y,
Evaluate tan x sin lim (0'0)+(^x)
Evaluate the limit or determine that it does not exist. lim (z,w)(-2,1) s(W) ez+w
Evaluate the limit or determine that it does not exist. lim (zw - 9z) (z,w) (-1,2)
Evaluate the limit or determine that it does not exist. lim (x,y) (4.2) y-2 x2 - 4 x
Evaluate the limit or determine that it does not exist. x + y lim (x,y)(0,0) 1 + y2
Evaluate the limit or determine that it does not exist. 1 lim (xy)+(3,4) x + y
Evaluate the limit or determine that it does not exist. lim (x,y)>(0,0) x + y2
Evaluate the limit or determine that it does not exist. COS X lim (x,y) (7,0) siny
Evaluate the limit or determine that it does not exist. lim (x,y)(0,0) cos x sin y y
Evaluate the limit or determine that it does not exist. lim (x,y) (1,-3) ex-y In(x - y)
Evaluate the limit or determine that it does not exist. |xx| lim (x,y)(0,0) [x] + [yl
Evaluate the limit or determine that it does not exist. (xy + 4xy) lim (x,y) (-3,-2)
Evaluate the limit or determine that it does not exist. e-t-y lim (x,y) (2,1)
Evaluate the limit or determine that it does not exist. lim tan(x + y) tan- (xy)(0,0) 1 x2 + y2
Evaluate the limit or determine that it does not exist. lim (x+y+2)e=/(x+y) (x,y) (0,0)
Evaluate the limit or determine that it does not exist. x + y lim (x,y) (0,0) x + y + 1 -1
Evaluate the limit or determine that it does not exist.Rewrite the limit in terms of u = x − 1 and v = y − 1. x + y - 2 lim (x,y) (1,1) |x-1| + y - 1|
Let (a) Show that(b) Show that |ƒ(x, y)| ≤ |x| + |y|.(c) Use the Squeeze Theorem to prove that f(x, y) = x + y x + y
Let a, b ≥ 0. Show that and that the limit does not exist if a + b ≤ 2. xyb lim (x,y) (0,0) x + y = 0 if a + b> 2
Figure 7 shows the contour maps of two functions. Explain why the limit in (A) does not exist. Does appear to exist in (B)? If so, what is its limit? lim_ f(x,y) (xy)
Evaluate (1 + x)y/x. lim (x,y) (0,2)
Is the following function continuous? x + y if x + y < 1 if x + y 1 f(x,y) = 3) = { + 3 1
The function ƒ(x, y) = sin(xy)/xy is defined for xy ≠ 0.(a) Is it possible to extend the domain of ƒ to all of R2 so that the result is a continuous function?(b) Use a computer algebra system to plot ƒ. Does the result support your conclusion in (a)?
Compute the first-order partial derivatives. - 2 X
Compute the first-order partial derivatives. Z = X x-y
Compute the first-order partial derivatives.z =√9 − x2 − y2
Compute the first-order partial derivatives. = 2 X x + y
Compute the first-order partial derivatives.z = (sin x)(cos y)
Compute the first-order partial derivatives.z = tan(uv3)
Compute the first-order partial derivatives. z = COS 1 - x y
Compute the first-order partial derivatives.θ = tan−1(xy2)
Compute the first-order partial derivatives.w = ln(x2 − y2)
Compute the first-order partial derivatives.P = sin(2s − 3t)
Compute the first-order partial derivatives.W = er+s
Compute the first-order partial derivatives.Q = reθ
Compute the first-order partial derivatives.z = exy
Compute the first-order partial derivatives.R = e−v2/k
Compute the first-order partial derivatives.z = e−x2−y2
Compute the first-order partial derivatives.P = e√y2+z2
Compute the first-order partial derivatives. U = en r
Compute the first-order partial derivatives.z = yx
Compute the first-order partial derivatives.z = sinh(x2y)
Compute the first-order partial derivatives.z = cosh(t − cos x)
Compute the first-order partial derivatives.w = xy2z3
Compute the first-order partial derivatives. W = X y + z
Compute the first-order partial derivatives. Q= L M -Lt/M
Compute the first-order partial derivatives. W = X (x + y +z)/2
Compute the given partial derivatives. f(x,y) = 3xy + 4xy - 7xys, fx(1,2)
Compute the given partial derivatives.g(u, v) = u ln(u + v), gu(1, 2)
Compute the given partial derivatives.h(x, z) = exz−x2z3 , hz(3, 0)
The heat index I is a measure of how hot it feels when the relative humidity is H (as a percentage) and the actual air temperature is T (in degrees Fahrenheit). An approximate formula for the heat index that is valid for (T, H) near (90, 40) is I(T,H) = 45.33 + 0.6845T +5.758H - 0.00365T - 0.1565HT
Calculate ∂P/∂T and ∂P/∂V, where pressure P, volume V, and temperature T are related by the Ideal Gas Law, PV = nRT (R and n are constants).
Showing 1300 - 1400
of 8339
First
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
Last
Step by Step Answers
Get 50% OFF
Claim Now
![(a) f(x,y) = x + [y] (b) f(x,y)= cos(x - y) -1 (c) f(x, y) = 1+9x + y (d) f(x, y) = cos(2)e-0.1(x +y) -1 (e)](https://dsd5zvtm8ll6.cloudfront.net/images/question_images/1704/6/9/4/910659b947e736b31704694909904.jpg)
![|xx| lim (x,y)(0,0) [x] + [yl](https://dsd5zvtm8ll6.cloudfront.net/images/question_images/1704/7/0/2/672659bb2d0c29da1704702672344.jpg)
![|x| |x|(x + y), ]y| [yl(x + y)](https://dsd5zvtm8ll6.cloudfront.net/images/question_images/1704/7/0/2/952659bb3e857b3b1704702951928.jpg){kind=small}
