Squeeze Theorem Calculator

This Squeeze Theorem Calculator helps users determine the limit of a middle function as x approaches a specific value by comparing it between two bounding functions.

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Step-by-Step Guide to Using the Squeeze Theorem Calculator

This guide will lead you through the process of using the Squeeze Theorem Calculator, an application designed to help you determine limits involving the squeeze theorem. Follow each step carefully to achieve accurate results.

Step 1: Select the Lower Function

  • Locate the field labeled Lower Function g(x).
  • Choose one of the available options from the dropdown menu: x, x², sin(x), or cos(x).
  • This selection represents the lower bounding function in your squeeze theorem problem.

Step 2: Select the Middle Function

  • Find the field labeled Middle Function h(x).
  • Select an option from the dropdown: x*sin(1/x), x²*cos(1/x), or x*cos(x).
  • This is the function you are primarily analyzing under the constraints of the squeeze theorem.

Step 3: Select the Upper Function

  • Navigate to the field labeled Upper Function f(x).
  • Choose a function from the options: x, x², sin(x), or cos(x).
  • This choice represents the upper bounding function in your analysis.

Step 4: Enter the x-value Approaching

  • Locate the field labeled x-value approaching.
  • Enter a numerical value indicating the point to which x is approaching.
  • The input should be a valid number and can be precise to four decimal places, if needed.

Step 5: Calculate the Limits

  • Once all selections and entries are complete, the calculator will automatically compute the limits of the selected functions as x approaches the specified value.
  • It will display the lower, middle, and upper function limits, each rounded to four decimal places.

Step 6: Interpret the Squeeze Theorem Result

  • The calculator applies the squeeze theorem to check if the middle limit falls between the lower and upper limits and if the lower and upper limits are equal.
  • The result will show the limit value if the conditions are satisfied, or it will indicate “Limit does not exist” if not.

Following these steps will ensure you utilize the Squeeze Theorem Calculator effectively to analyze the behavior of functions at given points. Remember, the key to using this tool accurately is ensuring all functions and values are correctly selected and entered.