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MTH1030 -1035 - Techniques for modelling - S1 2025
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, which is an indeterminate form. Applying L'Hôpital's rule once:
2. Now, when you substitute again, you get, which is still an indeterminate form. Therefore, we need to apply L'Hôpital's rule again:
3. As approaches 0, approaches 0, so the limit evaluates to.
Therefore, by applying L'Hôpital's rule twice, we find that the original limit is
.What is Of course, completely obvious. Still, nice to see that the theory works out.
Let and be differentiable functions for all real and let , and let the slope of at be 5 and the slope of at be 1. What is the slope of at 7.
What is
What’s special about Thomae’s function? That one here:
Tomae's function has a few more interesting properties than mentioned in in our write-up. Google Tomae's function and find out which of the following statements are true. There are a few, tick all.
A function is differentiable at if which of the following limits exists? Tick all that are correct.
Let be the function that is equal to 0 for all rational and 1 for every irrational . Is continuous at ?
What is