 3.1: Find points P and Q on the parabola y 1 2 x 2 so that the triangle ...
 3.2: Find the point where the curves y x 3 2 3x 1 4 and y 3sx 2 2 xd are...
 3.3: Show that the tangent lines to the parabola y ax 2 1 bx 1 c at any ...
 3.4: Show that d dx S sin2 x 1 1 cot x 1 cos2 x 1 1 tan x D 2cos 2x
 3.5: If fsxd lim tlx sec t 2 sec x t 2 x , find the value of f9sy4d.
 3.6: Find the values of the constants a and b such that lim xl0 s 3 ax 1...
 3.7: Show that sin21 stanh xd tan21 ssinh xd.
 3.8: A car is traveling at night along a highway shaped like a parabola ...
 3.9: Prove that dn dx n ssin4 x 1 cos4 xd 4n21 coss4x 1 ny2d.
 3.10: If f is differentiable at a, where a . 0, evaluate the following li...
 3.11: The figure shows a circle with radius 1 inscribed in the parabola y...
 3.12: Find all values of c such that the parabolas y 4x 2 and x c 1 2y 2 ...
 3.13: How many lines are tangent to both of the circles x 2 1 y 2 4 and x...
 3.14: If fsxd x 46 1 x 45 1 2 1 1 x , calculate f s46d s3d. Express your ...
 3.15: The figure shows a rotating wheel with radius 40 cm and a connectin...
 3.16: Tangent lines T1 and T2 are drawn at two points P1 and P2 on the pa...
 3.17: Show that dn dx n se ax sin bxd r n e ax sinsbx 1 nd
 3.18: Evaluate limxl esin x 2 1 x 2 .
 3.19: Let T and N be the tangent and normal lines to the ellipse x 2 y9 1...
 3.20: Evaluate limx l0 sins3 1 xd 2 2 sin 9 x .
 3.21: (a) Use the identity for tansx 2 yd (see Equation 14b in Appendix D...
 3.22: Let Psx1, y1d be a point on the parabola y 2 4px with focus Fsp, 0d...
 3.23: Suppose that we replace the parabolic mirror of by a spherical mirr...
 3.24: If f and t are differentiable functions with fs0d ts0d 0 and t9s0d ...
 3.25: Evaluate limx l0 sinsa 1 2xd 2 2 sinsa 1 xd 1 sin a x 2 .
 3.26: (a) The cubic function fsxd xsx 2 2dsx 2 6d has three distinct zero...
 3.27: For what value of k does the equation e2x ksx have exactly one solu...
 3.28: For which positive numbers a is it true that ax > 1 1 x for all x?
 3.29: If y x sa2 2 1 2 2 sa2 2 1 arctan sin x a 1 sa2 2 1 1 cos x show th...
 3.30: Given an ellipse x 2 ya2 1 y 2 yb2 1, where a b, find the equation ...
 3.31: Find the two points on the curve y x 4 2 2x 2 2 x that have a commo...
 3.32: Suppose that three points on the parabola y x 2 have the property t...
 3.33: A lattice point in the plane is a point with integer coordinates. S...
 3.34: A cone of radius r centimeters and height h centimeters is lowered ...
 3.35: A container in the shape of an inverted cone has height 16 cm and r...
Solutions for Chapter 3: Calculus 8th Edition
Full solutions for Calculus  8th Edition
ISBN: 9781285740621
Solutions for Chapter 3
Get Full SolutionsCalculus was written by and is associated to the ISBN: 9781285740621. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Calculus, edition: 8. Since 35 problems in chapter 3 have been answered, more than 9480 students have viewed full stepbystep solutions from this chapter. Chapter 3 includes 35 full stepbystep solutions.

Additive inverse of a complex number
The opposite of a + bi, or a  bi

Algebraic expression
A combination of variables and constants involving addition, subtraction, multiplication, division, powers, and roots

Branches
The two separate curves that make up a hyperbola

Compound fraction
A fractional expression in which the numerator or denominator may contain fractions

Constant
A letter or symbol that stands for a specific number,

Convergence of a sequence
A sequence {an} converges to a if limn: q an = a

Elements of a matrix
See Matrix element.

Equilibrium price
See Equilibrium point.

Equivalent arrows
Arrows that have the same magnitude and direction.

Gaussian elimination
A method of solving a system of n linear equations in n unknowns.

Irrational zeros
Zeros of a function that are irrational numbers.

Lower bound of f
Any number b for which b < ƒ(x) for all x in the domain of ƒ

Polynomial interpolation
The process of fitting a polynomial of degree n to (n + 1) points.

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

Response variable
A variable that is affected by an explanatory variable.

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

Solve by substitution
Method for solving systems of linear equations.

Terminal side of an angle
See Angle.

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

Weights
See Weighted mean.