All Matches

Solution Library

Expert Answer

Textbooks

Search Textbook questions, tutors and Books

Oops, something went wrong!

Change your search query and then try again

Result Not Found

Books FREE
Tutors
Study Help
Ask a Question
AI Study Help New

Search
Sign In
Register

study help
mathematics
precalculus

Questions and Answers of Precalculus

The contour map shows the average maximum temperature for November 2004 (in 8C). Estimate the value of the directional derivative of this temperature function at Dubbo, New South Wales, in the
Level curves for barometric pressure (in millibars) are shown for 6:00 am on a day in November. A deep low with pressure 972 mb is moving over northeast Iowa. The distance along the red line from K
Equation 6 is a formula for the derivative dy/dx of a function defined implicitly by an equation F(x, y) = 0, provided that F is differentiable and Fy ≠ 0. Prove that if F has continuous second
Suppose that the equation F(x, y, z) = 0 implicitly defines each of the three variables x, y, and z as functions of the other two:z = f (x, y), y = g(x, z), x = h( y, z). If F is differentiable and
If f is homogeneous of degree n, show that fx(tx, ty) = tn-1fx(x, y)
If f is homogeneous of degree n, show that д'f дх? д д'f + y?- ,2 ду? n(n — 1)/(х, у) + 2ху дх ду
A function f is called homogeneous of degree n if it satisfies the equation f (tx, ty) = tnf (x, y)for all t, where n is a positive integer and f has continuous second-order partial derivatives.(a)
Assume that all the given functions have continuous second-order partial derivatives.Suppose z = f (x, y), where x = g(s, t) and y = h(s, t).(a) Show that(b) Find a similar formula for ∂2z/∂s
Assume that all the given functions have continuous second-order partial derivatives. If z = f(x, y), where x = r cos 0 and y = r sin 0, find (a) dz/or, (b) dz/ae, and (c) a²z/dr d0.
Assume that all the given functions have continuous second-order partial derivatives.If z = f (x, y), where x = r2 + s2 and y = 2rs, find ∂2z/∂r ∂s. (Compare with Example 7.)
Assume that all the given functions have continuous second-order partial derivatives.If u = f (x, y), where x = es cos t and y = es sin t, show that д'и д'и ди а?и дs2 дг 2s дх? ду?
Assume that all the given functions have continuous second-order partial derivatives.Show that any function of the formz = f(x + at) + g(x - at)is a solution of the wave equation z. at? дх?
Assume that all the given functions are differentiable. If z =-[f(ax + y) + g(ax – y)], show that a? a a²z az у? ду дх? ду,
Assume that all the given functions are differentiable.If z = 1/x [f (x - y) + g(x + y)g, show that д?z д дz ду? x² дх Әх
Assume that all the given functions are differentiable.If u = f (x, y), where x = es cos t and y = es sin t, show that Не ди ди 2 ди -2я ди дs дt дх ду
A sound with frequency fs is produced by a source traveling along a line with speed vs. If an observer is traveling with speed vo along the same line from the opposite direction toward the source,
One side of a triangle is increasing at a rate of 3 cm/s and a second side is decreasing at a rate of 2 cm/s. If the area of the triangle remains constant, at what rate does the angle between the
A manufacturer has modeled its yearly production function P (the value of its entire production, in millions of dollars) as a Cobb-Douglas functionP(L, K) = 1.47L0.65K0.35where L is the number of
The pressure of 1 mole of an ideal gas is increasing at a rate of 0.05 kPa/s and the temperature is increasing at a rate of 0.15 K/s. Use the equation PV = 8.31T in Example 2 to find the rate of
The voltage V in a simple electrical circuit is slowly decreasing as the battery wears out. The resistance R is slowly increasing as the resistor heats up. Use Ohm’s Law, V = IR, to find how the
The length ℓ, width w, and height h of a box change with time. At a certain instant the dimensions are ℓ = 1 m and w = h = 2 m, and ℓ and w are increasing at a rate of 2 m/s while h is
The radius of a right circular cone is increasing at a rate of 1.8 in/s while its height is decreasing at a rate of 2.5 in/s. At what rate is the volume of the cone changing when the radius is 120
The speed of sound traveling through ocean water with salinity 35 parts per thousand has been modeled by the equationC = 1449.2 + 4.6T - 0.055T2 + 0.00029T3 + 0.016Dwhere C is the speed of sound (in
Wheat production W in a given year depends on the average temperature T and the annual rainfall R. Scientists estimate that the average temperature is rising at a rate of 0.15°C/year and rainfall is
The temperature at a point (x, y) is T(x, y), measured in degrees Celsius. A bug crawls so that its position after t seconds is given by x = √1 + t , y = 2 + 1/3 t, where x and y are measured in
Use Equations 7 to find ∂zy∂x and ∂z/∂y.yz + x ln y = z2
Use Equations 7 to find ∂zy∂x and ∂z/∂y.ez = xyz
Use Equations 7 to find ∂zy∂x and ∂z/∂y.x2 - y2 + z2 - 2z = 4
Use Equations 7 to find ∂zy∂x and ∂z/∂y.x2 + 2y2 + 3z2 = 1
Use Equation 6 to find dy/dx.ey sin x = x + xy
Use Equation 6 to find dy/dx.tan-1(x2y) = x + xy2
Use Equation 6 to find dy/dx.cos(xy) = 1 + sin y
Use Equation 6 to find dy/dx.y cos x = x2 + y2
Use the Chain Rule to find the indicated partial derivatives.
Use the Chain Rule to find the indicated partial derivatives. N= P + q p +r' p= u + vw, q = v + uw, r = w + uv; aN aN aN when u = 2, v = 3, w = 4 dv' dw ди
Use the Chain Rule to find the indicated partial derivatives. Р%3D и? + v? + w?, и — хе', v — уе*, w — е*%; ӘР ӘР дх ду when x = 0, y = 2
Use the Chain Rule to find the indicated partial derivatives. w 3 ху + уz + zx, х— rcos ®, у — r sin @, z — r0; ди ди when r - 2, Әө — п/2 дr
Use the Chain Rule to find the indicated partial derivatives.
Use the Chain Rule to find the indicated partial derivatives.
Use a tree diagram to write out the Chain Rule for the given case. Assume all functions are differentiable.R = F(t, u) where t = t (w, x, y, z), u = u(w, x, y, z)
Use a tree diagram to write out the Chain Rule for the given case. Assume all functions are differentiable.T = F(p, q, r), where p = p(x, y, z), q = q(x, y, z), r − r (x, y, z)
Use a tree diagram to write out the Chain Rule for the given case. Assume all functions are differentiable.w = f (x, y, z), where x = x(u, v), y = y(u, v), z = z(u, v)
Use a tree diagram to write out the Chain Rule for the given case. Assume all functions are differentiable.u = f (x, y), where x = x(r, s, t), y = y(r, s, t)
Suppose f is a differentiable function of x and y, and g(r, s) = f (2r - s, s2 - 4r). Use the table of values in Exercise 15 to calculate gr(1, 2) and gs(1, 2).
Use the Chain Rule to find ∂z/∂s and ∂z/∂t.z = √x exy, x = 1 + st, y = s2 - t2
Use the Chain Rule to find ∂z/∂s and ∂z/∂t.z = ln(3x + 2y), x = s sin t, y = t cos s
Use the Chain Rule to find ∂z/∂s and ∂z/∂t. z = tan-1(x2 + y2), x = s ln t, y = tes
Use the Chain Rule to find ∂z/∂s and ∂z/∂t.z = (x - y)5, x = s2t, y = st2
Use the Chain Rule to find dz/dt or dw/dt.w = ln√x2 + y2 + z2 , x = sin t, y = cos t, z = tan t
Use the Chain Rule to find dz/dt or dw/dt.w = xey/z, x = t2, y = 1 - t, z = 1 + 2t
Use the Chain Rule to find dz/dt or dw/dt.z = √1 + xy , x = tan t, y = arctan t
Use the Chain Rule to find dz/dt or dw/dt.z = sin x cos y, x = √t , y = 1/t
Use the Chain Rule to find dz/dt or dw/dt.z = xy3 - x2y, x = t2 + 1, y = t2 - 1
(a) The functionwas graphed in Figure 4. Show that fx(0, 0) and fy(0, 0) both exist but f is not differentiable at (0, 0). Use the result of Exercise 45.(b) Explain why fx and fy are not continuous
Prove that if f is a function of two variables that is differentiable at (a, b), then f is continuous at (a, b).Show that f(a + Ax, b + Ay) = f(a, b) lim (Ax, Ay)-(0, 0)
Show that the function is differentiable by finding values єof є1 and є2 that satisfy Definition 7.f (x, y) = x2 + y2
Suppose you need to know an equation of the tangent plane to a surface S at the point P(2, 1, 3). You don’t have an equation for S but you know that the curvesboth lie on S. Find an equation of the
In Exercise 14.1.39 and Example 14.3.3, the body mass index of a person was defined as B(m, h) = m/h2, where m is the mass in kilograms and h is the height in meters.(a) What is the linear
A model for the surface area of a human body is given by S = 0.1091w0.425h0.725, where w is the weight (in pounds), h is the height (in inches), and S is measured in square feet. If the errors in
If R is the total resistance of three resistors, connected in parallel, with resistances R1, R2, R3, then1/R = 1/R1 + 1/R2 + 1/R3If the resistances are measured in ohms as R1 = 25 Ω, R2 = 40 Ω, and
The pressure, volume, and temperature of a mole of an ideal gas are related by the equation PV = 8.31T, where P is measured in kilopascals, V in liters, and T in kelvins. Use differentials to find
The tension T in the string of the yo-yo in the figure isT = mtR/2r2 + R2where m is the mass of the yo-yo and g is acceleration due to gravity. Use differentials to estimate the change in the tension
The wind-chill index is modeled by the function W = 13.12 + 0.6215T - 11.37v0.16 + 0.3965Tv0.16where T is the temperature (in 8C) and v is the wind speed (in km/h). The wind speed is measured as
Use differentials to estimate the amount of tin in a closed tin can with diameter 8 cm and height 12 cm if the tin is 0.04 cm thick.
Use differentials to estimate the amount of metal in a closed cylindrical can that is 10 cm high and 4 cm in diameter if the metal in the top and bottom is 0.1 cm thick and the metal in the sides is
The length and width of a rectangle are measured as 30 cm and 24 cm, respectively, with an error in measurement of at most 0.1 cm in each. Use differentials to estimate the maximum error in the
If z = x2 - xy + 3y2 and (x, y) changes from (3, -1) to (2.96, 20.95), compare the values of Dz and dz.
If z = 5x2 + y2 and (x, y) changes from (1, 2) to (1.05, 2.1), compare the values of Dz and dz.
Find the differential of the function.L = xze-y2-z2
Find the differential of the function.T = v/1 + uvw
Find the differential of the function.m = p5q3
Find the differential of the function.u = √x2 + 3y2
The wind-chill index W is the perceived temperature when the actual temperature is T and the wind speed is v, so we can write W = f (T, v). The following table of values is an excerpt from Table 1 in
Use the table in Example 3 to find a linear approximation to the heat index function when the temperature is near 948F and the relative humidity is near 80%. Then estimate the heat index when the
The wave heights h in the open sea depend on the speed v of the wind and the length of time t that the wind has been blowing at that speed. Values of the function h = f (v, t) are recorded in feet in
Find the linear approximation of the function f (x, y, z) = (x2 + y2 + z2 at (3, 2, 6) and use it to approximate the number √(3.02)2 + (1.97)2 + (5.99)2 .
Given that f is a differentiable function with f (2, 5) = 6, fx(2, 5) = 1, and fy(2, 5) = -1, use a linear approximation to estimate f(2.2, 4.9).
Verify the linear approximation at (0, 0).y - 1/x + 1 ≈ x + y - 1
Verify the linear approximation at (0, 0).ex cos(xy) ≈ x + 1
Explain why the function is differentiable at the given point. Then find the linearization L(x, y) of the function at that point.f (x, y) = y + sin(x/y), (0, 3)
Explain why the function is differentiable at the given point. Then find the linearization L(x, y) of the function at that point.f (x, y) = 4 arctan(xy), (1, 1)
Explain why the function is differentiable at the given point. Then find the linearization L(x, y) of the function at that point.f (x, y) = 1 + y/1 + x , (1, 3)
Explain why the function is differentiable at the given point. Then find the linearization L(x, y) of the function at that point.f (x, y) = x2ey, (1, 0)
Explain why the function is differentiable at the given point. Then find the linearization L(x, y) of the function at that point.f (x, y) = √xy , (1, 4)
Explain why the function is differentiable at the given point. Then find the linearization L(x, y) of the function at that point.f (x, y) = 1 + x ln(xy - 5), (2, 3)
Draw the graph of f and its tangent plane at the given point. (Use your computer algebra system both to compute the partial derivatives and to graph the surface and its tangent plane.)Then zoom in
Draw the graph of f and its tangent plane at the given point. (Use your computer algebra system both to compute the partial derivatives and to graph the surface and its tangent plane.)Then zoom in
Graph the surface and the tangent plane at the given point. (Choose the domain and viewpoint so that you get a good view of both the surface and the tangent plane.) Then zoom in until the surface and
Graph the surface and the tangent plane at the given point. (Choose the domain and viewpoint so that you get a good view of both the surface and the tangent plane.) Then zoom in until the surface and
Find an equation of the tangent plane to the given surface at the specified point.z = ln(x - 2y), (3, 1, 0)
Find an equation of the tangent plane to the given surface at the specified point.z = x sin(x + y), (-1, 1, 0)
Find an equation of the tangent plane to the given surface at the specified point.z = x/y2, (-4, 2, -1)
Find an equation of the tangent plane to the given surface at the specified point.z = ex-y, (2, 2, 1)
Find an equation of the tangent plane to the given surface at the specified point.z = (x + 2)2 - 2( y - 1)2 - 5, (2, 3, 3)
Find an equation of the tangent plane to the given surface at the specified point.z = 2x2 + y2 - 5y, (1, 2, -4)
If f (x, y) = 3√x3 + y3 , find fx(0, 0).
If f(x, y) = x(x2 + y2)-3/2esin(x - y) find fx(1, 0).
(a) How many nth-order partial derivatives does a function of two variables have?(b) If these partial derivatives are all continuous, how many of them can be distinct?(c) Answer the question in part
Use Clairaut’s Theorem to show that if the third-order partial derivatives of f are continuous, thenfxyy = fyxy = fyyx
The ellipsoid 4x2 + 2y2 + z2 = 16 intersects the plane y = 2 in an ellipse. Find parametric equations for the tangent line to this ellipse at the point (1, 2, 2).

Showing 18300 - 18400 of 29459

First
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
Last

Services

Sitemap
Fun
Definitions
Become Tutor
Study Help Categories
Recent Questions
Expert Questions

Company Info

Security
Copyrights
Privacy Policy
Terms & Conditions
SolutionInn Fee
Scholarship

Get In Touch

About Us
Contact Us
Career
Jobs
FAQ
Campus Ambassador

Secure Payment

Download Our App

© 2024 SolutionInn. All Rights Reserved