 3.1: Firtd dy / dx in 1 through 35
 3.2: Firtd dy / dx in 1 through 36
 3.3: Firtd dy / dx in 1 through 37
 3.4: Firtd dy / dx in 1 through 38
 3.5: Firtd dy / dx in 1 through 39
 3.6: Firtd dy / dx in 1 through 40
 3.7: Firtd dy / dx in 1 through 41
 3.8: Firtd dy / dx in 1 through 42
 3.9: Firtd dy / dx in 1 through 43
 3.10: Firtd dy / dx in 1 through 44
 3.11: Firtd dy / dx in 1 through 45
 3.12: Firtd dy / dx in 1 through 46
 3.13: Firtd dy / dx in 1 through 47
 3.14: Firtd dy / dx in 1 through 48
 3.15: Firtd dy / dx in 1 through 49
 3.16: Firtd dy / dx in 1 through 50
 3.17: Firtd dy / dx in 1 through 51
 3.18: Firtd dy / dx in 1 through 52
 3.19: Firtd dy / dx in 1 through 53
 3.20: Firtd dy / dx in 1 through 54
 3.21: Firtd dy / dx in 1 through 55
 3.22: Firtd dy / dx in 1 through 56
 3.23: Firtd dy / dx in 1 through 57
 3.24: Firtd dy / dx in 1 through 58
 3.25: Firtd dy / dx in 1 through 59
 3.26: Firtd dy / dx in 1 through 60
 3.27: Firtd dy / dx in 1 through 61
 3.28: Firtd dy / dx in 1 through 62
 3.29: Firtd dy / dx in 1 through 63
 3.30: Firtd dy / dx in 1 through 64
 3.31: Firtd dy / dx in 1 through 65
 3.32: Firtd dy / dx in 1 through 66
 3.33: Firtd dy / dx in 1 through 67
 3.34: Firtd dy / dx in 1 through 68
 3.35: Firtd dy / dx in 1 through 69
 3.36: Find the derivatives of the functions defined in 36 through 45.
 3.37: Find the derivatives of the functions defined in 36 through 45.
 3.38: Find the derivatives of the functions defined in 36 through 45.
 3.39: Find the derivatives of the functions defined in 36 through 45.
 3.40: Find the derivatives of the functions defined in 36 through 45.
 3.41: Find the derivatives of the functions defined in 36 through 45.
 3.42: Find the derivatives of the functions defined in 36 through 45.
 3.43: Find the derivatives of the functions defined in 36 through 45.
 3.44: Find the derivatives of the functions defined in 36 through 45.
 3.45: Find the derivatives of the functions defined in 36 through 45.
 3.46: In 46 through 51. fnd dy/dx by implicit differentiation
 3.47: In 46 through 51. fnd dy/dx by implicit differentiation
 3.48: In 46 through 51. fnd dy/dx by implicit differentiation
 3.49: In 46 through 51. fnd dy/dx by implicit differentiation
 3.50: In 46 through 51. fnd dy/dx by implicit differentiation
 3.51: In 46 through 51. fnd dy/dx by implicit differentiation
 3.52: In 52 through 57. fnd dy/dx by logarithmic differentiation
 3.53: In 52 through 57. fnd dy/dx by logarithmic differentiation
 3.54: In 52 through 57. fnd dy/dx by logarithmic differentiation
 3.55: In 52 through 57. fnd dy/dx by logarithmic differentiation
 3.56: In 52 through 57. fnd dy/dx by logarithmic differentiation
 3.57: In 52 through 57. fnd dy/dx by logarithmic differentiation
 3.58: In 58 through 61, write an equation of the line tangent to the give...
 3.59: In 58 through 61, write an equation of the line tangent to the give...
 3.60: In 58 through 61, write an equation of the line tangent to the give...
 3.61: In 58 through 61, write an equation of the line tangent to the give...
 3.62: If a hemispherical bowl with radius I ft is filled with warer to a ...
 3.63: Falling sand forms a conical sandpile. Its height,h always remains ...
 3.64: Find the limits in 64 through 69.
 3.65: Find the limits in 64 through 69.
 3.66: Find the limits in 64 through 69.
 3.67: Find the limits in 64 through 69.
 3.68: Find the limits in 64 through 69.
 3.69: Find the limits in 64 through 69.
 3.70: In 70 through 75, identify the two functions f and g such that h(x)...
 3.71: In 70 through 75, identify the two functions f and g such that h(x)...
 3.72: In 70 through 75, identify the two functions f and g such that h(x)...
 3.73: In 70 through 75, identify the two functions f and g such that h(x)...
 3.74: In 70 through 75, identify the two functions f and g such that h(x)...
 3.75: In 70 through 75, identify the two functions f and g such that h(x)...
 3.76: The period ? ofoscillation (in seconds) ofa simple pendulum of leng...
 3.77: What is the rate of change of the volume V : jrrrr of a sphere with...
 3.78: What is an equation for the straight line through ( l. 0) thar is t...
 3.79: A rocket is launched vertically upward from a point 3 mi west of an...
 3.80: An oil field containing 20 wells has been producing 4000 banels of ...
 3.81: A tdangle is inscribed in a circle of radius R. One side of the tri...
 3.82: A tdangle is inscribed in a circle of radius R. One side of the tri...
 3.83: A mass of clay of volume V is formed into two spheres. For what dis...
 3.84: A right triangle has legs of lengths 3 m and 4 m. Whar is the maxim...
 3.85: What is the maximum possible volun]e of a right circular cone inscr...
 3.86: A farmer has 400 ft of f'encing with which to build a rect angular ...
 3.87: In one simple model of the spread of a contagious disease among mem...
 3.88: Three sidcs of a trapezoid have length L, a constant. What should b...
 3.89: A box with no top must have a base twice as long as it is wide. and...
 3.90: A small right circular cone is inscribed in a larger one (Fig. 3.MP...
 3.91: Two vertices of a trapezoid are at ( 2. 0) and (2. 0). and the oth...
 3.92: Suppose that I is a ditl'erentiable function defined on the whole r...
 3.93: Use the result of to show that the minimum dis tance from the point...
 3.94: A race track is to be built in the shape of two parallel and equal ...
 3.95: Two towns are located near the straight shore of a lake. Their near...
 3.96: A hiker finds herself in a lbrest 2 km from a long straight road. S...
 3.97: When an arrow is shot lioln the origin wirh initial veloc ity i, a...
 3.98: A projectile is tired with initial \elocity L'and angle of elevatio...
 3.99: In 99 through 110, use? Newton's method to find the solution of the...
 3.100: In 99 through 110, use? Newton's method to find the solution of the...
 3.101: In 99 through 110, use? Newton's method to find the solution of the...
 3.102: In 99 through 110, use? Newton's method to find the solution of the...
 3.103: In 99 through 110, use? Newton's method to find the solution of the...
 3.104: In 99 through 110, use? Newton's method to find the solution of the...
 3.105: In 99 through 110, use? Newton's method to find the solution of the...
 3.106: In 99 through 110, use? Newton's method to find the solution of the...
 3.107: In 99 through 110, use? Newton's method to find the solution of the...
 3.108: In 99 through 110, use? Newton's method to find the solution of the...
 3.109: In 99 through 110, use? Newton's method to find the solution of the...
 3.110: In 99 through 110, use? Newton's method to find the solution of the...
 3.111: Find the depth to which a wooden ball with radius 2 ft sinks in wat...
 3.112: The equation,r': + I : 0 has no real solutions. Try linding a solut...
 3.113: At the beginning of Section 3.10 we mentioned the lifthdegree equat...
 3.114: The equation tnn.t:1 has a sequence dl. dr. ai. ... of positive rco...
 3.115: Criticize the fbllowing "proof'that 3 = 2. Begin by writirlg .rr:.....
 3.116: show that :1 '_".t1 1 1),.rr:  Iim' ' i.,'t. ;.r2 [Srrggestioa...
 3.117: Prove that _t r _,.1 .1 D,.t: ' : lim :rJ [Saggestiol: Factor the...
 3.118: A rectangulal block with square base is being squeezed in such a wa...
 3.119: Air is being pumped into a spherical balloon at the constant rate o...
 3.120: A ladder 10 ft long is leaning against a wall. If the botrom of the...
 3.121: A water tank in the shape of an inverted cone. axis vertical and ve...
 3.122: Plane A is flying west toward an airport at an altitude of 2 mi. Pl...
 3.123: A water tank is shaped in such a way that the volume of water in th...
 3.124: Water is being poued into the conical tank of at the mte of 50 ft3l...
 3.125: Let L be a sfiaight line passing through the fixed point P(.r6,1,p)...
Solutions for Chapter 3: Calculus:Early Transcendentals 7th Edition
Full solutions for Calculus:Early Transcendentals  7th Edition
ISBN: 9780131569898
Solutions for Chapter 3
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Chapter 3 includes 125 full stepbystep solutions. This textbook survival guide was created for the textbook: Calculus:Early Transcendentals, edition: 7. Calculus:Early Transcendentals was written by and is associated to the ISBN: 9780131569898. Since 125 problems in chapter 3 have been answered, more than 9298 students have viewed full stepbystep solutions from this chapter.

Common ratio
See Geometric sequence.

Composition of functions
(f ? g) (x) = f (g(x))

Equivalent systems of equations
Systems of equations that have the same solution.

Fitting a line or curve to data
Finding a line or curve that comes close to passing through all the points in a scatter plot.

Hyperboloid of revolution
A surface generated by rotating a hyperbola about its transverse axis, p. 607.

Identity function
The function ƒ(x) = x.

Implicitly defined function
A function that is a subset of a relation defined by an equation in x and y.

Independent variable
Variable representing the domain value of a function (usually x).

Linear function
A function that can be written in the form ƒ(x) = mx + b, where and b are real numbers

LRAM
A Riemann sum approximation of the area under a curve ƒ(x) from x = a to x = b using x1 as the lefthand endpoint of each subinterval

Main diagonal
The diagonal from the top left to the bottom right of a square matrix

Mathematical induction
A process for proving that a statement is true for all natural numbers n by showing that it is true for n = 1 (the anchor) and that, if it is true for n = k, then it must be true for n = k + 1 (the inductive step)

Ordered pair
A pair of real numbers (x, y), p. 12.

Periodic function
A function ƒ for which there is a positive number c such that for every value t in the domain of ƒ. The smallest such number c is the period of the function.

Positive angle
Angle generated by a counterclockwise rotation.

Removable discontinuity at x = a
lim x:a ƒ(x) = limx:a+ ƒ(x) but either the common limit is not equal ƒ(a) to ƒ(a) or is not defined

Sphere
A set of points in Cartesian space equally distant from a fixed point called the center.

Upper bound for ƒ
Any number B for which ƒ(x) ? B for all x in the domain of ƒ.

Variance
The square of the standard deviation.

Vertex of a parabola
The point of intersection of a parabola and its line of symmetry.