By Stan Gibilisco

Master calculus from the relaxation of home!

Want to "know all of it" in terms of calculus? This e-book promises the specialist, one-on-one guideline you wish, even if you are new to calculus or you are looking to ramp up your talents. offering easy-to-understand techniques and carefully defined workouts, math whiz Stan Gibilisco serves as your individual inner most tutor--without the price! His transparent, pleasant counsel is helping you take on the techniques and difficulties that confuse you the main and paintings via them at your personal velocity.

Train your mind comfortably! Calculus Know-It-ALL gains:

  • Checkpoints that will help you music your wisdom and ability level
  • Problem/solution pairs and chapter-ending quizzes to augment studying
  • Fully defined solutions to all perform routines
  • A multiple-choice examination to organize you for standardized exams
  • "Extra credits" and "Challenge" difficulties to stretch your mind

Stan's professional information promises the knowledge to:

  • Understand mappings, relatives, and functions
  • Calculate limits and be sure continuity
  • Differentiate and combine functions
  • Analyze graphs utilizing first and moment derivatives
  • Define and overview inverse functions
  • Use really expert integration techniques
  • Determine arc lengths, floor parts, and sturdy volumes
  • Work with multivariable functions
  • Take university front examinations with self belief
  • And a lot more!

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Additional resources for Calculus know-it-all: beginner to advanced, and everything in between

Example text

Consider the following linear function: f (x ) = 4x − 5 What is the inverse of this? Is it a function? Practice Exercises 19 4. Consider the following linear function: g (x ) = 7 What is the inverse of this? Is it a function? 5. In the Cartesian coordinate xy plane, the equation of a circle with radius 1, centered at the origin (0,0), is x2 + y2 = 1 This particular circle is called the unit circle. Is its equation a function of x ? If so, why? If not, why not? 6. Is the equation of the unit circle, as expressed in Prob.

7. Consider the nonlinear function we graphed in Fig. 1-6: g (x) = x 2 As we saw, the inverse relation, g−1, is not a function. But it can be modified so it becomes a function of x by restricting its range to the set of positive real numbers. Show with the help of a graph why this is true. Does g−1 remain a function if we allow the range to include 0? 8. We can modify the relation g−1 from the previous problem, making it into a function of x, by restricting its range to the set of negative real numbers.

Broken" Functions 15 y 6 4 y = –3 if x < 0 y = 0 if x = 0 y = 3 if x > 0 2 x –6 –4 –2 2 4 6 –2 –4 –6 Figure 1-8 Graph of the “broken” function y = −3 if x < 0, y = 0 if x = 0, y = 3 if x > 0. A three-part function Figure 1-8 is a graph of a function where the value is −3 if the argument is negative, 0 if the argument is 0, and 3 if the argument is positive. Let’s call the function f. Then we can write f (x ) = −3 if x < 0 = 0 if x = 0 = 3 if x > 0 Even though this function takes two jumps, there are no gaps in the domain.

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