Find limits numerically by analyzing a table of values.

Problem

Dragomir wants to find limx05x23xx\displaystyle \lim_{x\to 0}\dfrac{5x^2-3x}{x}.
His table below shows values of f, left parenthesis, x, right parenthesis, equals, start fraction, 5, x, start superscript, 2, end superscript, minus, 3, x, divided by, x, end fraction for x-values that get increasingly closer to 0:
xf, left parenthesis, x, right parenthesis
0, point, 1minus, 2, point, 5000
0, point, 01minus, 2, point, 9500
0, point, 001minus, 2, point, 9950
0question mark
minus, 0, point, 001minus, 3, point, 0050
minus, 0, point, 01minus, 3, point, 0500
minus, 0, point, 1minus, 3, point, 5000
From the table, what does limx05x23xx\displaystyle \lim_{x\to 0}\dfrac{5x^2-3x}{x} appear to be?
  • Your answer should be
  • an integer, like 6
  • an exact decimal, like 0, point, 75
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4