Find limits numerically by analyzing a table of values.

Problem

Nahnatchka wants to find limx1sin(5x5)x1\displaystyle \lim_{x\to 1}\dfrac{\sin(5x-5)}{x-1}.
Her table below shows values of h, left parenthesis, x, right parenthesis, equals, start fraction, sine, left parenthesis, 5, x, minus, 5, right parenthesis, divided by, x, minus, 1, end fraction for x-values that get increasingly closer to 1:
xh, left parenthesis, x, right parenthesis
1, point, 14, point, 79426
1, point, 014, point, 99792
1, point, 0014, point, 99998
1question mark
0, point, 9994, point, 99998
0, point, 994, point, 99792
0, point, 94, point, 79426
From the table, what does limx1sin(5x5)x1\displaystyle \lim_{x\to 1}\dfrac{\sin(5x-5)}{x-1} 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