# Calculus Demystified: A Self Teaching Guide

## Steven G. Krantz

Language: English

Pages: 355

ISBN: B00M3ULGOY

Format: PDF / Kindle (mobi) / ePub

* Explains how to understand calculus in a more intuitive fashion

* Uses practical examples and real data

* Covers both differential and integral calculus

Fractals, Googols, and Other Mathematical Tales

Post-Modern Algebra (Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts)

A Course in Commutative Algebra (Graduate Texts in Mathematics, Volume 256)

The Language of Mathematics: Utilizing Math in Practice

Final Exam 317 (c) f −1 (x) = x 3 − x f −1 (d) (x) = x/(x + 1 ) (e) f −1 (x) = x 3 − 1 3 · b−2 a 21. The expression ln simplifies to c 4 /d−3 (a) 3 ln a − 2 ln b − 4 ln c + 3 ln d (b) 3 ln a + 2 ln b + 4 ln c − 3 ln d (c) 4 ln a − 3 ln b + 2 ln c − 4 ln d (d) 3 ln a − 4 ln b + 3 ln c − 2 ln d (e) 4 ln a − 2 ln b + 2 ln c + 2 ln d 22. The expression e ln a 2−ln b 3 simplifies to (a) 2 a · 3 b 2 a (b) 3 b (c) a 2 · b 3 2 a (d) b 3 2 b 3 (e) 6 a x 2 if x < 1

23. The function f (x) = has limits x if x ≥ 1 (a) 2 at c = 1 and −1 at c = 0 (b) 1 at c = 1 and 4 at c = −2 (c) 0 at c = 0 and 3 at c = 5 (d) −3 at c = −3 and 2 at c = 1 (e) 1 at c = 0 and 2 at c = 2 x 24. The function f (x) = has limits x 2 − 1 (a) 3 at c = 1 and 2 at c = −1 (b) ∞ at c = 1 and 0 at c = −1 (c) 0 at c = 0 and nonexistent at c = ±1 (d) 2 at c = −2 and −2 at c = 2 (e) −∞ at c = 1 and +∞ at c = −1 x 3 if x < 2 25. The function f (x) = √ is

2 x − 1 2 −1 1 1 (b) ln | x − 1| − + ln | x + 1| + C 2 (x − 1 ) 2 2 −1 1 1 (c) ln | x − 1| + + ln | x + 1| + C 2 x − 1 4 −1 1 1 (d) ln | x − 1| − + ln | x + 1| + C 2 x − 1 2 −1 1 / 2 1 (e) ln | x − 1| − + ln | x + 1| + C 4 x − 1 4 √ 2 87. The value of the integral x 1 + x 2 dx is 1 Final Exam 333 (a) 1 53 / 2 − 1 23 / 2 4 4 (b) 1 43 / 2 − 1 33 / 2 3 3 (c) 1 53 / 2 − 1 23 / 2 3 3 (d) 1 43 / 2 − 1 33 / 2 5 5 (e) 1 23 / 2 − 1 53 / 2 3

plane that is a square with center the origin and vertices on the axes. The vertical slice parallel to the y-axis is an equilateral triangle. What is the volume? √ 2 3 (a) 3 Final Exam 335 √ 3 (b) 3 √ (c) 3 √ (d) 3 + 3 √ (e) 3 3 95. The planar region bounded by y = x 2 and y = x is rotated about the line y = −1. What volume results? 11 π (a) 15 7 π (b) 15 7 π (c) 19 8 π (d) 15 2 π (e) 15 √ 96. The planar region bounded by y = x and y = x is rotated about

Chapter 5 - Indeterminate Forms Chapter 6 - Transcendental Functions Chapter 7 - Methods of Integration Chapter 8 - Applications of the Integral Bibliography Solutions to Exercises Final Exam Solutions