Today:
- Announcements
- We have homework due today (related rates).
- Today we will do one more example of Section 2.8 related rates, and then move on to Section 2.9: linear approximations.
- Examples:
- #23 (similar triangles)
- #31 (ladders! Pythagoras.... This one sounds like a joke! "What color is the bear?")
- #34
- In section 2.9, we use the tangent line to make certain approximations.
- For example, suppose you need to compute $\sqrt{15.96}$. Now the
easy way is to use your calculator, but the cowboy way would be to use
the linearization! Let's have a go at that one.
- We know the square root of 16, which is close: our answer should be near 4.
- Draw a picture! The picture will demonstrate two different
types of quantities that we discuss in this chapter:
differentials $dy$, and increments $\Delta y$.
- We use the tangent line for our approximation, and, when
we're done, we can ask
- is our answer an over- or an under-estimate?
- Examples
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