MediumMathematicsHigh School (11–12)Functions and Calculus › Limits and DerivativesNumerical

Two sensors on a small rotating arm give the readings s = sin 5t and r = tan 2t, where t is the…

Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

Two sensors on a small rotating arm give the readings $s = \sin 5t$ and $r = \tan 2t$ , where $t$ is the angle of the arm in radians. Both readings are almost zero when the arm is almost at rest. A technician forms the ratio $\dfrac{s}{r}$ and asks what value it approaches as $t$ tends to $0$ . Find that value. The angle is in radians throughout.

Need a reminder? The key ideaShow

With $x$ in radians: $\dfrac{\sin x}{x} \to 1$ and $\dfrac{\tan x}{x} \to 1$ as $x \to 0$ ; $\dfrac{x^n - a^n}{x - a} \to na^{n-1}$ as $x \to a$ ; $\dfrac{a^x - 1}{x} \to \ln a$ as $x \to 0$ .

The worked solution

Have you tried it?

Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

← All Problems

← A designer draws the curve y = √(x² + 6x) for x > 0, with lengths in metres (m), and the straight…A lab compares two cultures. After x hours the first has 3ˣ million cells and the second has 2ˣ… →

More onFunctions and Calculus › Limits and Derivatives

Discussion (0)

Loading…