Practice question · Estimate
Numerically explore as (radians): compute it mentally for small , then set the slider to the limit.
Estimate on a scale from 0 to 2.
Hints
- Try : . Divide.
- For tiny angles, the arc and its sine are nearly the same length, so their ratio approaches…
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1 (answers within ±0.1 count)
Why
The ratio squeezes to exactly 1: for small angles, . This limit is the seed of all trigonometric calculus, the derivative of sine at 0, and the reason pendulum formulas work for small swings.
Practise Limits and continuity
The app has 8 more questions on this lesson, and keeps your place in the course. Physics I is free to start.
More questions on Limits and continuity
- Sort these functions based on the type of discontinuity.
- A function satisfies f(2) = 5, but lim x→ 2 f(x) = 3. What does the graph look like near x = 2?
- A function can have a limit of 5 at x = 2 while f(2) = 9, or while f(2) does not exist at all. What does that…
- Order the steps in an epsilon-delta proof that lim x→ a f(x) = L.
- Sort each function by what happens at the marked point.