Question

Consider function (x) = (x)co(x), for any x ∊ (set of all real numbers). In each task (T1), … , (T5) provide a short answer including justification.

(T1) Identify all roots of (x), i.e., all points x ∊ for which (x) = 0.

Answer 1

To find the roots of the misprinted function f(x) = x*co(x), we assumed a correction to x*cos(x). In this case, the roots are x where x=0 or cos(x)=0 in the interval [0, 20]. The precise identification of all roots requires the correct function expression.

Step-by-step explanation:

To find the roots of the function f(x) = xco(x), we need to determine the values of x for which f(x) = 0. However, the expression provided in the question does not correspond to a standard mathematical function, and seems to be a typographical error. Assuming it might be a misrepresentation of xcos(x), we would proceed by looking for values of x where either x = 0 or cos(x) = 0 within the given domain of 0 ≤ x ≤ 20.

The roots where x = 0 is one root. The roots where cos(x) = 0 occur at odd multiples of π/2 within the allowed domain. Consequently, the specific roots would be π/2, 3π/2, 5π/2, etc., up to the largest odd multiple of π/2 that is less than or equal to 20. Note that x cannot be negative since we are restricted to the domain 0 ≤ x ≤ 20.

Without additional context or correction of the original function, a precise identification of all roots is not feasible. For educational purposes and understanding the concept, the example provided assumes the correct interpretation of the function and demonstrates the approach to solve it.