Practice question · True or false
The linear approximation is exact for a linear function and only approximate for every other.
Hints
- What does the error term contain?
- exactly when is linear.
Show the answer
True
Why
True. Taylor's remainder is , which vanishes identically only when the second derivative is zero, that is, for a linear . Everything else carries an error growing with the square of the distance at a rate set by the curvature.
Practise Curve Sketching
The app has 5 more questions on this lesson, and keeps your place in the course. Mathematics I is free to start.
More questions on Curve Sketching
- Order the curve-sketching checklist.
- Engineers replace sin θ with θ for small angles, and pendulum clocks work because of it. What is being…
- Let f(x) = (x + 1)/(x - 3). Select every TRUE statement about its graph.
- Newton's method finds a root by repeatedly stepping along the tangent line: x − f(x)/f'(x). Why does…
- Sort each function by its symmetry.