 13.7.1: Suppose that f (1, 0, 1) = 2, and f (x, y, z) is differentiableat(1...
 13.7.2: Suppose that f (x, y)is differentiable at the point(3, 1) withf (3,...
 13.7.3: An equation for the tangent plane to the graph of z = x2yat the poi...
 13.7.4: The sphere x2 + y2 + z2 = 9 and the plane x + y + z = 5intersect in...
 13.7.5: 312 Find an equation for the tangent plane and parametricequations ...
 13.7.6: 312 Find an equation for the tangent plane and parametricequations ...
 13.7.7: 312 Find an equation for the tangent plane and parametricequations ...
 13.7.8: 312 Find an equation for the tangent plane and parametricequations ...
 13.7.9: 312 Find an equation for the tangent plane and parametricequations ...
 13.7.10: 312 Find an equation for the tangent plane and parametricequations ...
 13.7.11: 312 Find an equation for the tangent plane and parametricequations ...
 13.7.12: 312 Find an equation for the tangent plane and parametricequations ...
 13.7.13: Find all points on the surface at which the tangent planeis horizon...
 13.7.14: Find a point on the surface z = 3x2 y2 at which thetangent plane is...
 13.7.15: Find a point on the surface z = 8 3x2 2y2 at whichthe tangent plane...
 13.7.16: Show that the surfacesz =x2 + y2 and z = 110 (x2 + y2) + 52intersec...
 13.7.17: (a) Find all points of intersection of the linex = 1 + t, y = 2 + t...
 13.7.18: Show that if f is differentiable and z = xf(x/y), then alltangent p...
 13.7.19: 1922 TrueFalse Determine whether the statement is true orfalse. Exp...
 13.7.20: 1922 TrueFalse Determine whether the statement is true orfalse. Exp...
 13.7.21: 1922 TrueFalse Determine whether the statement is true orfalse. Exp...
 13.7.22: 1922 TrueFalse Determine whether the statement is true orfalse. Exp...
 13.7.23: 2324 Find two unit vectors that are normal to the given surfaceat t...
 13.7.24: 2324 Find two unit vectors that are normal to the given surfaceat t...
 13.7.25: Show that every line that is normal to the spherex2 + y2 + z2 = 1pa...
 13.7.26: Find all points on the ellipsoid 2x2 + 3y2 + 4z2 = 9 atwhich the pl...
 13.7.27: Find all points on the surface x2 + y2 z2 = 1 at which thenormal li...
 13.7.28: Show that the ellipsoid 2x2 + 3y2 + z2 = 9 and the spherex2 + y2 + ...
 13.7.29: Find parametric equations for the tangent line to the curve ofinter...
 13.7.30: Find parametric equations for the tangent line to the curveof inter...
 13.7.31: Find parametric equations for the tangent line to the curve ofinter...
 13.7.32: The accompanying figure shows the intersection of the surfacesz = 8...
 13.7.33: Show that the equation of the plane that is tangent to theellipsoid...
 13.7.34: Show that the equation of the plane that is tangent to theparaboloi...
 13.7.35: Prove: If the surfaces z = f(x, y) and z = g(x, y) intersectat P (x...
 13.7.36: Use the result in Exercise 35 to show that the normal lines tothe c...
 13.7.37: Two surfaces f(x, y, z) = 0 and g(x, y, z) = 0 are said tobe orthog...
 13.7.38: Use the result of Exercise 37 to show that the spherex2 + y2 + z2 =...
 13.7.39: Show that the volume of the solid bounded by the coordinateplanes a...
 13.7.40: Writing Discuss the role of the chain rule in defining atangent pla...
 13.7.41: Writing Discuss the relationship between tangent planesand local li...
Solutions for Chapter 13.7: TANGENT PLANES AND NORMAL VECTORS
Full solutions for Calculus: Early Transcendentals,  10th Edition
ISBN: 9780470647691
Solutions for Chapter 13.7: TANGENT PLANES AND NORMAL VECTORS
Get Full SolutionsCalculus: Early Transcendentals, was written by and is associated to the ISBN: 9780470647691. Chapter 13.7: TANGENT PLANES AND NORMAL VECTORS includes 41 full stepbystep solutions. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, , edition: 10. This expansive textbook survival guide covers the following chapters and their solutions. Since 41 problems in chapter 13.7: TANGENT PLANES AND NORMAL VECTORS have been answered, more than 39927 students have viewed full stepbystep solutions from this chapter.

Cofunction identity
An identity that relates the sine, secant, or tangent to the cosine, cosecant, or cotangent, respectively

Convenience sample
A sample that sacrifices randomness for convenience

Difference of functions
(ƒ  g)(x) = ƒ(x)  g(x)

Exponential function
A function of the form ƒ(x) = a ? bx,where ?0, b > 0 b ?1

Frequency (in statistics)
The number of individuals or observations with a certain characteristic.

Grapher or graphing utility
Graphing calculator or a computer with graphing software.

Histogram
A graph that visually represents the information in a frequency table using rectangular areas proportional to the frequencies.

Order of magnitude (of n)
log n.

Permutations of n objects taken r at a time
There are nPr = n!1n  r2! such permutations

Positive association
A relationship between two variables in which higher values of one variable are generally associated with higher values of the other variable, p. 717.

Powerreducing identity
A trigonometric identity that reduces the power to which the trigonometric functions are raised.

Product of a scalar and a vector
The product of scalar k and vector u = 8u1, u29 1or u = 8u1, u2, u392 is k.u = 8ku1, ku291or k # u = 8ku1, ku2, ku392,

Real number
Any number that can be written as a decimal.

Reflexive property of equality
a = a

Richter scale
A logarithmic scale used in measuring the intensity of an earthquake.

Sinusoidal regression
A procedure for fitting a curve y = a sin (bx + c) + d to a set of data

Slant line
A line that is neither horizontal nor vertical

Standard form of a polynomial function
ƒ(x) = an x n + an1x n1 + Á + a1x + a0

Standard unit vectors
In the plane i = <1, 0> and j = <0,1>; in space i = <1,0,0>, j = <0,1,0> k = <0,0,1>

Vertical line
x = a.