 2.6.1: Assume that x4 f (x) x2. What is limx0 f (x)? Is there enough infor...
 2.6.2: State the Squeeze Theorem carefully.
 2.6.3: If you want to evaluate limh0 sin 5h 3h , it is a good idea to rewr...
 2.6.4: Determine limx0 f (x) assuming that cos x f (x) 1.
 2.6.5: State whether the inequality provides sufficient information to det...
 2.6.6: Plot the graphs of u(x) = 1 + x 2 and l(x) = sin x on the same set ...
 2.6.7: In Exercises 716, evaluate using the Squeeze Theorem. lim x0 x2 cos...
 2.6.8: In Exercises 716, evaluate using the Squeeze Theorem. lim x0 x sin ...
 2.6.9: In Exercises 716, evaluate using the Squeeze Theorem. lim x1 (x 1)s...
 2.6.10: In Exercises 716, evaluate using the Squeeze Theorem. lim x3 (x2 9)...
 2.6.11: In Exercises 716, evaluate using the Squeeze Theorem. lim t0 (2t 1)...
 2.6.12: In Exercises 716, evaluate using the Squeeze Theorem. lim x0+ x eco...
 2.6.13: In Exercises 716, evaluate using the Squeeze Theorem. lim t2 (t2 4)...
 2.6.14: In Exercises 716, evaluate using the Squeeze Theorem. lim x0 tan x ...
 2.6.15: In Exercises 716, evaluate using the Squeeze Theorem. lim 2 cos cos...
 2.6.16: In Exercises 716, evaluate using the Squeeze Theorem. lim t0+ sin t...
 2.6.17: In Exercises 1726, evaluate using Theorem 2 as necessary. lim x0 ta...
 2.6.18: In Exercises 1726, evaluate using Theorem 2 as necessary. lim x0 si...
 2.6.19: In Exercises 1726, evaluate using Theorem 2 as necessary. lim t0 t3...
 2.6.20: In Exercises 1726, evaluate using Theorem 2 as necessary. lim t0 si...
 2.6.21: In Exercises 1726, evaluate using Theorem 2 as necessary. lim x0 x2...
 2.6.22: In Exercises 1726, evaluate using Theorem 2 as necessary. lim t 2 1...
 2.6.23: In Exercises 1726, evaluate using Theorem 2 as necessary. lim 0 sec 1
 2.6.24: In Exercises 1726, evaluate using Theorem 2 as necessary. lim 0 1 c...
 2.6.25: In Exercises 1726, evaluate using Theorem 2 as necessary. lim t 4 s...
 2.6.26: In Exercises 1726, evaluate using Theorem 2 as necessary. lim t0 co...
 2.6.27: Let L = lim x0 sin 14x x . (a) Show, by letting = 14x, that L = lim...
 2.6.28: Evaluate lim h0 sin 9h sin 7h . Hint: sin 9h sin 7h = 9 7 sin 9h 9h...
 2.6.29: In Exercises 2948, evaluate the limit. lim h0 sin 9h h
 2.6.30: In Exercises 2948, evaluate the limit. im h0 sin 4h 4h
 2.6.31: In Exercises 2948, evaluate the limit. lim h0 sin h 5h
 2.6.32: In Exercises 2948, evaluate the limit. lim x 6 x sin 3x
 2.6.33: In Exercises 2948, evaluate the limit. lim 0 sin 7 sin 3
 2.6.34: In Exercises 2948, evaluate the limit. lim x0 tan 4x 9x
 2.6.35: In Exercises 2948, evaluate the limit. lim x0 x csc 25x
 2.6.36: In Exercises 2948, evaluate the limit. lim t0 tan 4t t sec t
 2.6.37: In Exercises 2948, evaluate the limit. lim h0 sin 2h sin 3h h2
 2.6.38: In Exercises 2948, evaluate the limit. lim z0 sin(z/3) sin z
 2.6.39: In Exercises 2948, evaluate the limit. lim 0 sin(3 ) sin(4 )
 2.6.40: In Exercises 2948, evaluate the limit. lim x0 tan 4x tan 9x
 2.6.41: In Exercises 2948, evaluate the limit. lim t0 csc 8t csc 4t
 2.6.42: In Exercises 2948, evaluate the limit. lim x0 sin 5x sin 2x sin 3x ...
 2.6.43: In Exercises 2948, evaluate the limit. lim x0 sin 3x sin 2x x sin 5x
 2.6.44: In Exercises 2948, evaluate the limit. lim h0 1 cos 2h h
 2.6.45: In Exercises 2948, evaluate the limit. lim h0 sin(2h)(1 cos h) h2 4
 2.6.46: In Exercises 2948, evaluate the limit. lim t0 1 cos 2t sin2 3t
 2.6.47: In Exercises 2948, evaluate the limit. lim 0 cos 2 cos
 2.6.48: In Exercises 2948, evaluate the limit. lim h 2 1 cos 3h h
 2.6.49: Calculate lim x0 sin x x
 2.6.50: Use the identity sin 3 = 3 sin 4 sin3 to evaluate the limit lim 0 s...
 2.6.51: Prove the following result: lim 0 csc cot = 0
 2.6.52: Investigate limh0 1 cos h h2 numerically (and graphically if you ha...
 2.6.53: In Exercises 5355, evaluate using the result of Exercise 52. lim h0...
 2.6.54: In Exercises 5355, evaluate using the result of Exercise 52. lim h0...
 2.6.55: In Exercises 5355, evaluate using the result of Exercise 52. lim t0...
 2.6.56: Use the Squeeze Theorem to prove that if limxc f (x) = 0, then li...
 2.6.57: Use the result of Exercise 52 to prove that for m = 0, lim x0 cos m...
 2.6.58: Using a diagram of the unit circle and the Pythagorean Theorem, sho...
 2.6.59: (a) Investigate limxc sin x sin c x c numerically for the five valu...
Solutions for Chapter 2.6: Trigonometric Limits
Full solutions for Calculus: Early Transcendentals  3rd Edition
ISBN: 9781464114885
Solutions for Chapter 2.6: Trigonometric Limits
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Since 59 problems in chapter 2.6: Trigonometric Limits have been answered, more than 42097 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals , edition: 3. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9781464114885. Chapter 2.6: Trigonometric Limits includes 59 full stepbystep solutions.

Associative properties
a + (b + c) = (a + b) + c, a(bc) = (ab)c.

Backtoback stemplot
A stemplot with leaves on either side used to compare two distributions.

Coordinate(s) of a point
The number associated with a point on a number line, or the ordered pair associated with a point in the Cartesian coordinate plane, or the ordered triple associated with a point in the Cartesian threedimensional space

Derivative of ƒ
The function defined by ƒ'(x) = limh:0ƒ(x + h)  ƒ(x)h for all of x where the limit exists

End behavior asymptote of a rational function
A polynomial that the function approaches as.

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.

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

Increasing on an interval
A function ƒ is increasing on an interval I if, for any two points in I, a positive change in x results in a positive change in.

Irrational zeros
Zeros of a function that are irrational numbers.

Leastsquares line
See Linear regression line.

Magnitude of a vector
The magnitude of <a, b> is 2a2 + b2. The magnitude of <a, b, c> is 2a2 + b2 + c2

nth root of a complex number z
A complex number v such that vn = z

Onetoone rule of logarithms
x = y if and only if logb x = logb y.

Parallel lines
Two lines that are both vertical or have equal slopes.

Partial fraction decomposition
See Partial fractions.

Polar coordinates
The numbers (r, ?) that determine a point’s location in a polar coordinate system. The number r is the directed distance and ? is the directed angle

Power regression
A procedure for fitting a curve y = a . x b to a set of data.

Scalar
A real number.

Square matrix
A matrix whose number of rows equals the number of columns.

Trigonometric form of a complex number
r(cos ? + i sin ?)