Limits &concepts of functions

 

 

 

Course :

 

For Pre-calculus students

Created by Kameswari Tekumalla for Synergy Project (Mar 6th)

Uses Web links produced by Stefan Warner, Steven R. Cosenoble , and Lawrence S. Husch

 

 

Background

 

Most applications in calculus deal with continuous functions, but the visualization of processes often starts with finite changes in the variables of interest. One power of calculus is that it can deal with changes which are infinitesimally small. For example, an average velocity is obtained by taking a distance traveled and dividing it by the finite time interval it took to travel that distance. But suppose you wanted the instantaneous velocity at a given instant of time. You can approach that with a "limit," i.e., you can take the smaller distances traveled in shorter intervals and divide by those shorter times. If this process is allowed to continue until the time interval approaches zero, then this is called "taking the limit as the time interval approaches zero." This is the way a derivative of distance with respect to time is defined, and the way that an instantaneous velocity is calculated using calculus methods. Limits are also used in the formation of integrals, or anti-derivatives.  To learn more about them visit the websites Graphical Approach

Numerical Approach, and Algebraic Approach.

 

 

 

QUESTIONS:

 

Q1.  Verify the following limits using the Function Evaluator as well as the Algebraic

         method.

 

   

. .                                                          

 

                           

 

                                          

 

 

Q2.  Business: If you deposit $1 into a bank account paying 10% interest compounded        

        continuously, a year later its value will be  .

 

      Find the limit by making a table of values (close to zero) using the

       Function Evaluator correct to two decimal places thereby finding the value of the  

       deposit in dollars and cents. 

 

 

Q3.  Find   using  Function Evaluator  correct to three decimal places.