 8.7.1: lim x0 sin 4x sin 3x
 8.7.2: lim x0 1 ex x
 8.7.3: lim x x5 ex 100
 8.7.4: lim x 6x 3x2 2x
 8.7.5: lim x4 3x 4 x2 16
 8.7.6: lim x2 2x2 x 6 x 2
 8.7.7: lim x6 x 10 4 x 6
 8.7.8: lim x0 sin 6x 4x
 8.7.9: lim x 5x2 3x 1 3x2 5
 8.7.10: lim x 2x 1 4x2 x
 8.7.11: lim x3 x2 2x 3 x 3
 8.7.12: lim x1 x2 2x 3 x 1
 8.7.13: lim x0 25 x2 5 x
 8.7.14: lim x5 25 x2 x 5
 8.7.15: lim x0 ex 1 x x
 8.7.16: lim x1 ln x2 x2 1
 8.7.17: lim x0 ex 1 x x3
 8.7.18: lim x0 ex 1 x xn
 8.7.19: lim , x1 x11 1 x4 1
 8.7.20: lim a, b 0 x1 xa 1 xb 1 lim ,
 8.7.21: lim , x0 sin 3x sin 5x
 8.7.22: lim a, b 0 x0 sin ax sin bx
 8.7.23: lim x0 arcsin x x
 8.7.24: lim x1 arctan x 4 x 1
 8.7.25: lim x 5x2 3x 1 4x2 5
 8.7.26: lim x x 6 x2 4x 7
 8.7.27: lim x x2 4x 7 x 6
 8.7.28: lim x x3 x 2
 8.7.29: lim 2 x x3 ex 2
 8.7.30: lim x x3 ex lim 2
 8.7.31: lim x x x2 1
 8.7.32: lim x x2 x2 1
 8.7.33: lim x cos x x
 8.7.34: lim x sin x x
 8.7.35: lim x ln x x2
 8.7.36: lim x ln x4 x3
 8.7.37: lim x ex x4
 8.7.38: lim x e x 2 x
 8.7.39: lim x0 sin 5x tan 9x
 8.7.40: lim x1 ln x sin x
 8.7.41: lim x0 arctan x sin x
 8.7.42: lim x0 x arctan 2x
 8.7.43: lim x x 1 lne4t1 dt x
 8.7.44: lim x1 x 1 cos d x 1
 8.7.45: In Exercises 4562, (a) describe the type of indeterminate form (if ...
 8.7.46: In Exercises 4562, (a) describe the type of indeterminate form (if ...
 8.7.47: In Exercises 4562, (a) describe the type of indeterminate form (if ...
 8.7.48: In Exercises 4562, (a) describe the type of indeterminate form (if ...
 8.7.49: In Exercises 4562, (a) describe the type of indeterminate form (if ...
 8.7.50: In Exercises 4562, (a) describe the type of indeterminate form (if ...
 8.7.51: In Exercises 4562, (a) describe the type of indeterminate form (if ...
 8.7.52: In Exercises 4562, (a) describe the type of indeterminate form (if ...
 8.7.53: In Exercises 4562, (a) describe the type of indeterminate form (if ...
 8.7.54: In Exercises 4562, (a) describe the type of indeterminate form (if ...
 8.7.55: In Exercises 4562, (a) describe the type of indeterminate form (if ...
 8.7.56: In Exercises 4562, (a) describe the type of indeterminate form (if ...
 8.7.57: In Exercises 4562, (a) describe the type of indeterminate form (if ...
 8.7.58: In Exercises 4562, (a) describe the type of indeterminate form (if ...
 8.7.59: In Exercises 4562, (a) describe the type of indeterminate form (if ...
 8.7.60: In Exercises 4562, (a) describe the type of indeterminate form (if ...
 8.7.61: In Exercises 4562, (a) describe the type of indeterminate form (if ...
 8.7.62: In Exercises 4562, (a) describe the type of indeterminate form (if ...
 8.7.63: lim x3 x 3 ln2x 5
 8.7.64: lim x0 sin xx
 8.7.65: lim x x2 5x 2 x
 8.7.66: lim x x3 e2x
 8.7.67: List six different indeterminate forms.
 8.7.68: State LHpitals Rule.
 8.7.69: Find differentiable functions and that satisfy the specified condit...
 8.7.70: Find differentiable functions and such that and Explain how you obt...
 8.7.71: Complete the table to show that eventually overpowers
 8.7.72: Complete the table to show that eventually overpowers
 8.7.73: lim x x2 e5x
 8.7.74: lim x x3 e2x
 8.7.75: lim x ln x3 x
 8.7.76: lim x ln x2 x3
 8.7.77: lim x ln xn xm
 8.7.78: lim x xm enx
 8.7.79: In Exercises 7982, find any asymptotes and relative extrema that ma...
 8.7.80: In Exercises 7982, find any asymptotes and relative extrema that ma...
 8.7.81: In Exercises 7982, find any asymptotes and relative extrema that ma...
 8.7.82: In Exercises 7982, find any asymptotes and relative extrema that ma...
 8.7.83: In Exercises 8387, LHpitals Rule is used incorrectly. Describe the ...
 8.7.84: In Exercises 8387, LHpitals Rule is used incorrectly. Describe the ...
 8.7.85: In Exercises 8387, LHpitals Rule is used incorrectly. Describe the ...
 8.7.86: In Exercises 8387, LHpitals Rule is used incorrectly. Describe the ...
 8.7.87: In Exercises 8387, LHpitals Rule is used incorrectly. Describe the ...
 8.7.88: Determine which of the following limits can be evaluated using LHpi...
 8.7.89: lim x x x2 1
 8.7.90: lim x 2 tan x sec x
 8.7.91: fx sin 3x, gx sin 4x
 8.7.92: fx e gx x 3x 1
 8.7.93: The velocity of an object falling through a resisting medium such a...
 8.7.94: The formula for the amount in a savings account compounded times pe...
 8.7.95: The Gamma Function is defined in terms of the integral of the funct...
 8.7.96: A person moves from the origin along the positive axis pulling a we...
 8.7.97: In Exercises 97100, apply the Extended Mean Value Theorem to the fu...
 8.7.98: In Exercises 97100, apply the Extended Mean Value Theorem to the fu...
 8.7.99: In Exercises 97100, apply the Extended Mean Value Theorem to the fu...
 8.7.100: In Exercises 97100, apply the Extended Mean Value Theorem to the fu...
 8.7.101: lim x0 x2 x 1 x lim x0 2x 1 1 1
 8.7.102: In Exercises 101104, determine whether the statement is true or fal...
 8.7.103: In Exercises 101104, determine whether the statement is true or fal...
 8.7.104: In Exercises 101104, determine whether the statement is true or fal...
 8.7.105: Find the limit, as approaches 0, of the ratio of the area of the tr...
 8.7.106: In Section 1.3, a geometric argument (see figure) was used to prove...
 8.7.107: fx 4x 2 sin 2x 2x3 , c, x 0 x 0
 8.7.108: fx ex x1 x , c, x 0 x 0
 8.7.109: Find the values of and such that limx0 a cos bx x a b 2 2.
 8.7.110: Show that for any integer n > 0
 8.7.111: a) Let be continuous. Show that (b) Explain the result of part (a) ...
 8.7.112: Let be continuous. Show that limh0 fx h 2fx fx h h2 f x.
 8.7.113: Sketch the graph of gx e1 x 2 0, , x 0 x 0 and determine g0.
 8.7.114: Use a graphing utility to graph for 0.1, and 0.01. Then evaluate th...
 8.7.115: Consider the limit (a) Describe the type of indeterminate form that...
 8.7.116: Prove that if fx 0, fx 0,and then lim xa fxgx 0.
 8.7.117: Prove that if and then lim xa fxgx .
 8.7.118: Prove the following generalization of the Mean Value Theorem. If is...
 8.7.119: Show that the indeterminate forms and do not always have a value of...
 8.7.120: In LHpitals 1696 calculus textbook, he illustrated his rule using t...
 8.7.121: Consider the function (a) Use a graphing utility to graph the funct...
 8.7.122: Let and (a) Show that (b) Show that and (c) Evaluate the limit What...
 8.7.123: Evaluate lim a > 0, a 1. x 1 x ax 1 a 1 1 x
Solutions for Chapter 8.7: Indeterminate Forms and LHpitals Rule
Full solutions for Calculus  9th Edition
ISBN: 9780547167022
Solutions for Chapter 8.7: Indeterminate Forms and LHpitals Rule
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Chapter 8.7: Indeterminate Forms and LHpitals Rule includes 123 full stepbystep solutions. Calculus was written by and is associated to the ISBN: 9780547167022. Since 123 problems in chapter 8.7: Indeterminate Forms and LHpitals Rule have been answered, more than 68190 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Calculus , edition: 9.

Absolute value of a complex number
The absolute value of the complex number z = a + b is given by ?a2+b2; also, the length of the segment from the origin to z in the complex plane.

Ambiguous case
The case in which two sides and a nonincluded angle can determine two different triangles

Annual percentage rate (APR)
The annual interest rate

Bounded interval
An interval that has finite length (does not extend to ? or ?)

Completing the square
A method of adding a constant to an expression in order to form a perfect square

Convergence of a series
A series aqk=1 ak converges to a sum S if imn: q ank=1ak = S

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

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

Graph of parametric equations
The set of all points in the coordinate plane corresponding to the ordered pairs determined by the parametric equations.

Intermediate Value Theorem
If ƒ is a polynomial function and a < b , then ƒ assumes every value between ƒ(a) and ƒ(b).

Inverse tangent function
The function y = tan1 x

Lower bound test for real zeros
A test for finding a lower bound for the real zeros of a polynomial

Major axis
The line segment through the foci of an ellipse with endpoints on the ellipse

Parallelogram representation of vector addition
Geometric representation of vector addition using the parallelogram determined by the position vectors.

Polynomial function
A function in which ƒ(x)is a polynomial in x, p. 158.

Power rule of logarithms
logb Rc = c logb R, R 7 0.

Real zeros
Zeros of a function that are real numbers.

Standard form: equation of a circle
(x  h)2 + (y  k2) = r 2

Xscl
The scale of the tick marks on the xaxis in a viewing window.

yintercept
A point that lies on both the graph and the yaxis.