MATH110 April 2016
• Q1 (a) • Q1 (b) • Q1 (c) • Q1 (d) • Q2 (a) • Q2 (b) • Q2 (c) • Q2 (d) • Q3 (a) • Q3 (b) • Q3 (c) • Q4 (a) • Q4 (b) • Q4 (c) • Q4 (d) • Q5 (a) • Q5 (b) • Q5 (c) • Q5 (d) • Q5 (e) • Q5 (f) • Q5 (g) • Q5 (h) • Q5 (i) • Q6 (a) • Q6 (b) • Q7 • Q8 (a) • Q8 (b) • Q8 (c) • Q8 (d) • Q9 (a) • Q9 (b) • Q10 •
Question 08 (a)
(a) Use an appropriate linear approximation to estimate . Simplify your answer.
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!
Try using a linear approximation. You should set and center your approximation around .
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We want to approximate the value
To this end, we define the function .
We will use a linear approximation:
We want to use and . It is necessary to compute . The derivative of is
and we get the approximation
This is believable because we expect to get something just a little less than , since we are dividing by a number that is just a little more than 4.