Science:Math Exam Resources/Courses/MATH104/December 2015/Question 05 (a)
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Question 05 (a) |
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Use linear approximation to estimate the value of State your answer accurate to two decimal places. |
Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you? |
If you are stuck, check the hints below. Read the first one and consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! If after a while you are still stuck, go for the next hint. |
Hint 1 |
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A simple way of approximating is to construct the linear approximation of (i.e., tangent line to) at some point for which is known exactly and |
Hint 2 |
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Observe that and and follow the suggestion in hint 1. |
Hint 3 |
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Recall that the equation of the line tangent to at is This is also known as the linear approximation of at
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Checking a solution serves two purposes: helping you if, after having used all the hints, you still are stuck on the problem; or if you have solved the problem and would like to check your work.
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Solution |
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Found a typo? Is this solution unclear? Let us know here.
Please rate my easiness! It's quick and helps everyone guide their studies. The linear approximation to a function at is In this problem, we are asked to use a linear approximation to We choose to approximate at because and is exactly known and easy to work with. Thus our approximation is Now so Hence Plugging in gives |