Final answer:
With the given functions f and g, we can find limits, derivatives, and check continuity, but we may not be able to find integrals analytically, possibly requiring numerical methods.
Step-by-step explanation:
The question asks what cannot be done with the functions f = (x³+y³)^(1/3) and g = e^(-1/x²). These functions involve operations like taking cube roots and exponentials, which are well-defined mathematical operations. Therefore, we can generally:
- Find limits, as both functions have well-defined behavior at many points, although there may be certain points where the limits do not exist or are not finite.
- Find derivatives, as both functions can be differentiated using the rules of calculus, provided we are not at a point of discontinuity or undefined expression in the case of g when x=0.
- Find continuity, by checking if the function is unbroken and well-defined over its domain.
However, finding the integrals analytically for these functions may not always be possible due to their complex nature, and we might need to resort to numerical methods or express the result in terms of non-elementary functions.