Problem 1E: In Exercises 1–10, find equations for the
tangent plane and
normal line at the point P0 on the given... Problem 2E: In Exercises 1–10, find equations for the
tangent plane and
normal line at the point P0 on the given... Problem 3E: In Exercises 1–10, find equations for the
tangent plane and
normal line at the point P0 on the given... Problem 4E: In Exercises 1–10, find equations for the
tangent plane and
normal line at the point P0 on the given... Problem 5E: In Exercises 1–10, find equations for the
tangent plane and
normal line at the point P0 on the given... Problem 6E: In Exercises 1–10, find equations for the
tangent plane and
normal line at the point P0 on the given... Problem 7E: In Exercises 1–10, find equations for the
tangent plane and
normal line at the point P0 on the given... Problem 8E: In Exercises 1–10, find equations for the
tangent plane and
normal line at the point P0 on the given... Problem 9E: In Exercises 1–10, find equations for the
tangent plane and
normal line at the point P0 on the given... Problem 10E: In Exercises 1–10, find equations for the
tangent plane and
normal line at the point P0 on the given... Problem 11E: In Exercises 11–14, find an equation for the plane that is tangent to the given surface at the given... Problem 12E: In Exercises 11–14, find an equation for the plane that is tangent to the given surface at the given... Problem 13E: In Exercises 11–14, find an equation for the plane that is tangent to the given surface at the given... Problem 14E: In Exercises 11–14, find an equation for the plane that is tangent to the given surface at the given... Problem 15E: In Exercises 15–20, find parametric equations for the line tangent to the curve of intersection of... Problem 16E: In Exercises 15–20, find parametric equations for the line tangent to the curve of intersection of... Problem 17E: In Exercises 15–20, find parametric equations for the line tangent to the curve of intersection of... Problem 18E: In Exercises 15–20, find parametric equations for the line tangent to the curve of intersection of... Problem 19E: In Exercises 15–20, find parametric equations for the line tangent to the curve of intersection of... Problem 20E: In Exercises 15–20, find parametric equations for the line tangent to the curve of intersection of... Problem 21E Problem 22E Problem 23E: By about how much will
change if the point P(x, y, z) moves from P0(2, –1, 0) a distance of ds =... Problem 24E Problem 25E: Temperature change along a circle Suppose that the Celsius temperature at the point (x, y) in the... Problem 26E: Changing temperature along a space curve The Celsius temperature in a region in space is given by .... Problem 27E: In Exercises 27–32, find the linearization L(x, y) of the function at each point.
27. at
(0,... Problem 28E: In Exercises 27–32, find the linearization L(x, y) of the function at each point.
28. at
(0,... Problem 29E: In Exercises 27–32, find the linearization L(x, y) of the function at each point.
29. at
(0,... Problem 30E: In Exercises 27–32, find the linearization L(x, y) of the function at each point.
30. at
(1,... Problem 31E: In Exercises 27–32, find the linearization L(x, y) of the function at each point.
31. at
(0, 0),
Problem 32E: In Exercises 27–32, find the linearization L(x, y) of the function at each point.
32. at
(0,... Problem 33E: Wind chill factor Wind chill, a measure of the apparent temperature felt on exposed skin, is a... Problem 34E: Find the linearization L(v, T) of the function W(v, T) in Exercise 33 at the point (50, –20). Use it... Problem 35E: In Exercises 35-40, find the linearization L(x, y) of the function f(x, y) at P0. Then find an upper... Problem 36E: In Exercises 35-40, find the linearization L(x, y) of the function f(x, y) at P0. Then find an upper... Problem 37E: In Exercises 35-40, find the linearization L(x, y) of the function f(x, y) at P0. Then find an upper... Problem 38E: In Exercises 35-40, find the linearization L(x, y) of the function f(x, y) at P0. Then find an upper... Problem 39E Problem 40E: In Exercises 35-40, find the linearization L(x, y) of the function f(x, y) at P0. Then find an upper... Problem 41E: Find the linearizations L(x, y, z) of the functions in Exercises 41-46 at the given points.
41. f(x,... Problem 42E: Find the linearizations L(x, y, z) of the functions in Exercises 41-46 at the given points.
42. f(x,... Problem 43E Problem 44E Problem 45E Problem 46E Problem 47E Problem 48E: In Exercises 47-50, find the linearization L(x, y, z) of the function f(x, y, z) at P0. Then find an... Problem 49E Problem 50E Problem 51E: Estimating maximum error Suppose that T is to be found from the formula T = x(ey + e‒y), where x and... Problem 52E Problem 53E Problem 54E Problem 55E Problem 56E Problem 57E Problem 58E: Change along the involute of a circle Find the derivative of f(x, y) = x2 + y2 in the direction of... Problem 59E: Tangent curves A smooth curve is tangent to the surface at a point of intersection if its velocity... Problem 60E: Normal curves A smooth curve is normal to a surface f(x, y, z) = c at a point of intersection if the... Problem 61E: Consider a closed rectangular box with a square base, as shown in the figure. Assume x is measured... format_list_bulleted