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This is really not a Math test question bt could be one - like cuz it relates to whatever is being asked in math...

1. If f '(x) and g '(x) exist and f '(x) > g '(x) for all real [unparseable or potentially dangerous latex formula]. then the graph of [unparseable or potentially dangerous latex formula] and the graph of [unparseable or potentially dangerous latex formula]

A. intersect exactly once
B. intersec no more than once
C. do not intersect
D. could intersect more than once
E. have a common tangent at each point of intersection


2. What is the amplitude of the function [unparseable or potentially dangerous latex formula] ?

Thanks.. And I did forget to mention that the answer is B...

For [unparseable or potentially dangerous latex formula] why can't u do [unparseable or potentially dangerous latex formula] ?
These two yield different answers - one of them being right - the one w/out simplification of integrand (is that what u call it?).

The range of [unparseable or potentially dangerous latex formula] is limited to [unparseable or potentially dangerous latex formula], whereas the range of [unparseable or potentially dangerous latex formula] is all real numbers. [unparseable or potentially dangerous latex formula] is always positive as we cannot have a negative result when finding the square root of something. Since [unparseable or potentially dangerous latex formula] is negative when [unparseable or potentially dangerous latex formula], yet [unparseable or potentially dangerous latex formula] is positive when [unparseable or potentially dangerous latex formula], but both are basically the same function, and due to the fact that [unparseable or potentially dangerous latex formula] is a radical and [unparseable or potentially dangerous latex formula] is the simplification of [unparseable or potentially dangerous latex formula], [unparseable or potentially dangerous latex formula]

Thus: [unparseable or potentially dangerous latex formula]