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Skill check: Finding limits

Consider the table with function values for f(t)=t32t2+1t31f(t)=\dfrac{t^3-2t^2+1}{t^3-1} at tt-values near 11. There is one value missing in the table.
Use a calculator to evaluate f(t)f(t) at t=1.0001t=1.0001, and enter this number in the table rounded through 66 significant figures.
From the table, what does
limt1t32t2+1t31\qquad \displaystyle \lim_{t\to 1}\dfrac{t^3-2t^2+1}{t^3-1}
appear to be?
ttf(t)f(t)
0.990.990.340022-0.340022
0.9990.9990.334000-0.334000
0.99990.99990.333400-0.333400
1.00011.0001
  • Your answer should be
  • an integer, like 66
  • an exact decimal, like 0.750.75
  • a simplified proper fraction, like 3/53/5
  • a simplified improper fraction, like 7/47/4
  • a mixed number, like 1 3/41\ 3/4
1.0011.0010.332667-0.332667
1.011.010.326689-0.326689
Choose 1 answer:
Choose 1 answer: