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Estimating Limits with Technology
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Calculus I
CAL1.45 Estimating Limits with Technology
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A spreadsheet estimates f(x) = (1 + x)^(1/x) for x near 0 from both sides where the expression is defined. Values such as 2.7048 and 2.7319 appear near x = +/-0.01. Which option gives the best estimate and explanation?
A
Estimate 1; the base approaches 1.
B
Estimate 0; the exponent 1/x becomes unbounded.
C
DNE; positive and negative x-values give different nearby decimals.
D
Estimate about 2.71828; the function approaches e, and the two sides differ slightly because the sampled x-values are nonzero.
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