Limit at infinity
Instructions: 1. Enter any function you like in the text box. 2. Uncheck 'enter function' after entering the function to check if your input has been successfully recognized. 3. Hold down 'shift' and drag to adjust the view if necessary. You can also adjust the scale by holding down 'shift' and drag the axis. 4. Move further and further towards the right by dragging or arrow keys on your keyboard. Notice how the value of y, as given by the limit changes. If the limit at infinity exist, you should observe that the value of y gets closer and closer towards a certain value. 5. (Finding a limit by graphical method) Hold down 'shift' an drag the x-axis to bring a larger x be shown in view. If the limit at infinity exist, you may observe that the function becomes more and more like an (imaginary) straight horizontal line on the right hand side of the graph. This line is called the horizontal asymptote. Confirm your imagination by checking the 'show horizontal asymptote box'. 6. Check 'show limit at infinity' to confirm your observations in step 4 and step 5. 7. Repeat steps 1 to 8 if necessary.
Tasks: Try the following functions: 1. 100000/1.02^(x) 2. 1/(1-e^(-x)) 3. 1/x 4. Any logistic function (e.g. 100/(1-2e^(-0.5x)) ) 5. Any rational function (e.g. (x+1)/(x-1) ) 6. e^x (Note: the limit at infinity does not exist for this function) 7. ln(x) (Note: the limit at infinity does not exist for this function) Created for SCNC1111 Calculus Tutorials Applicable topics: L3. Limit at infinity