一道SAT2数学题及其解法.

　　下面是一道SAT2数学题及其解法的相关信息，这是一道关于函数方面的SAT2数学题，属于Level2方面的，难度并不大，但是对大家的逻辑思维水平还是有一些要求的。下面是详细内容，供大家参考，可以先做一下题目，然后在看看解释。

　　If , what value does approach as gets infinitely larger?

　　Answer Choices

　　(A)

　　(B)

　　(C)

　　(D)

　　(E)

　　The correct answer is E.

　　Explanation

　　Difficulty: Easy

　　One way to determine the value that approaches as gets infinitely larger is to rewrite the dinition of the function to use only negative powers of and then reason about the behavior of negative powers of as gets infinitely larger. Since the question is only concerned with what happens to as gets infinitely larger, one can assume that is positive. For , the expression is equivalent to the expression . As gets infinitely larger, the expression approaches the value , so as gets infinitely larger, the expression approaches the value . Thus, as gets infinitely larger, approaches .

　　Alternatively, one can use a graphing calculator to estimate the height of the horizontal asymptote for the function . Graph the function on an interval with “large” , say, from to .　　

　　By examining the graph, the all seem very close to . Graph the function again, from, say, to .　　

　　The vary even less from . In fact, to the scale of the coordinate plane shown, the graph of the functionis nearly indistinguishable from the asymptotic line . This suggests that as gets infinitely larger, approaches , that is, .

　　Note: The algebraic method is prerable, as it provides a proof that guarantees that the value approaches is . Although the graphical method worked in this case, it does not provide a complete justification; for example, the graphical method does not ensure that the graph resembles a horizontal line for “very large” such as .

　　以上就是这道SAT2数学题，后面包括了解法，非常详细，以文字和图片两种形式来解析的。SAT2数学考试分成了两个Level，大家可以根据自己的需要选择合适自己的考试项目进行适当的备考。

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