what is an object?
An object is an instance of the class. A more real world example of an object may be a TV for example. The TV object would be just one TV of a single design of multiple designs (classes of TVs) and the one TV in your room would be an instance of that design. The TV would have data such as what channel you're currently on, and methods or actions such as on/off and changing the channel or calling up the guide menu.
take the limit as x approaches 0 of sin(x)/x
This question requirers L'Hospital's rule which says that the limit of a function in the form of f(x)/g(x) is equal to the derivative of f(x) over the derivative of g(x) or f'(x)/g'(x). in the case that a limit turns out to be indeterminate such as 0/0 or inf/inf this is rather useful. in this case, where sin(0)/0 turns out to be 0/0 we differentiate sin(x) to cos(x) and x to 1 where the new limit is the limit as x approaches 0 of cos(x) which is 1
Solve for x^2+2x-3=0
This question may be answered with the quadratic formula with 2 for b, 1 for a, and -3 for c, but is much more easily done with factoring by realizing that -1 * 3 = -3 for c and -1 + 3 = 2 for b. Thus, this is simplified to (x-1)(x+3)=0 which we can tell equals zero when one factor is zero, so the answers are x=1 and x=-3