Idon’t understand the question can someone me ?

That "double" less than symbol is used to say "much smaller than". It is of course a qualitative symbol, and it has no rigorous definition.

The exercise asks you to verify, numerically, that if you choose a very, very small input, then the approximations are good. Take the first one for example: we claim that if we pick a very small angle, its cosine is almost one. Let's choose . If we compute its cosine, we have

So, approximating the result with 1 is a good approximation.

Similarly, in the second example, we claim that for very small angles, the sine of the angle is almost the angle itself: choosing for example , we have

So the output is almost identically to the input.

For the third, we claim that and are almost the same thing if x is very small. So, for example, we pick and we have

whereas

so the two results are almost identical.

You can keep going like this and "prove" all the remaining approximations

im here

step-by-step explanation: