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How do I Solve Word Problems in Calculus?

A word problem, a math exercise that presents the problem in text form rather than in mathematical notation, can be difficult for students because they first must translate the text into numbers in order to solve the equation. To solve a calculus word problem, you must be able to identify the information the problem gives and the information you need to solve for.
  1. Read the Problem

    • Read the entire problem first. This will keep you from missing key information. As you read, look for the facts given in the word problem relevant to solving the equation. List the information you identify on paper. Write out any equations given to you in the problem alongside the facts. Pulling the information out of the word problem helps you to focus on the numbers, eliminating the words that can obscure the question.

    Organization

    • Organize the information you pulled from the text. Drawing a diagram, constructing a table or plotting points on a graph will allow you to organize the given information in an easy-to-read graphic. Determine what information you are trying to solve for once you have organized all of the facts and equations. Often, word problems have several potential answers, but by determining what the question is asking, you can eliminate any unnecessary work.

    Identification

    • Use the given information to reduce the number of unknown variables. Identify what the unknown variables are by using your knowledge of how rates relate to each other. Determine if a given rate can help you ascertain an unknown rate in the equation. Identify what the relationship is between the given rate and the unknown rate. Once you have identified this relationship, write out an equation that relates the given information to the unknown variables.

    Solve the Equation

    • Solve the equation to determine the answer. Once you have finished your calculations, double check your work to make sure you followed the correct order of operations. Ask yourself if your answer makes sense in relation to the question. Does your answer find what the word problem asked you to solve for and do the numbers in your answer make sense? If you are satisfied that your answer correctly satisfies everything the word problem asked you to find, then consider the problem solved and move on the next equation.

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