Science:Math Exam Resources/Courses/MATH100 B/December 2023/Question 21
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Question 21 

Estimate the solution to the differential equation using one step of size with an intial condition . 
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 hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! 
Hint 

Taylor series are often used to estimate functions. 
Checking a solution serves two purposes: helping you if, after having used the hint, you still are stuck on the problem; or if you have solved the problem and would like to check your work.

Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. Recall that the Taylor series for a function is We are given , , and we have an equation for . Substituting this all in gives The solution is approximately . 