clear all ; Read this file into Mathomatic to learn how the limit command does limits. ; The formula for the derivative of a function of "x" (f(x)) is: ; f(x+h) - f(x) ; limit ------------- As "h" goes to 0. ; h ; Here we will compute the derivative of "x^.5" using limits: y=((x+h)^.5-x^.5)/h limit h 0 ; Take the limit of the current equation as "h" goes to 0. ; The result should be "y = 1/(2*x^0.5)". pause ; To show how the limit command works, we will do what it does, step by step. 1 ; Select the original equation (equation number 1). ; We want "h" to go to 0 to give us the derivative. ; Just entering 0 for "h" will give a divide by zero error. ; So we will first have to solve for "h": h pause ; Simplify and replace "h" with 0: simplify symbolic replace h with 0 pause ; Last step, solve the equation back for "y": y compare 1 with 2 ; Compare with the result of the limit command. ; Obviously this method only works if the equation is solvable. pause ; INFINITY LIMITS ; --------------- ; To take the limit as some variable "h" goes to infinity, ; remember that 1/infinity is essentially 0, and the limit ; of "1/h" as "h" goes to 0 is +/-infinity, so replace "h" ; with "1/h" and take the limit as "h" now goes to 0. ; Note that this method doesn't always work and sometimes gives wrong answers. ; Let's try a simple example: y=(5x+100-a)/(x-b) limit x inf ; Take the limit as "x" goes to infinity. ; The limit command should say the result is 5. pause ; To show how the limit command works, we will do what it does, step by step. 3 ; Select the original equation (equation number 3). ; To take the limit as "x" approaches infinity, ; first replace "x" with "1/x": replace x with 1/x pause ; Simplify and replace "x" with 0: simplify replace x with 0 ; The result should be 5.