Question
Use your calculator to generate a table of values to help you estimate the value for the limit
Use your calculator to generate a table of values to help you estimate the value for the limit
lim (e^h - 1) /h
h approaches 0
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Koala Tutor
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To generate a table of values, we can choose a range of values for h and calculate the corresponding values for the expression (e^h - 1) / h using a calculator:
h= 0.1 | (e^h - 1) / h ≈ 0.105170918
h= 0.01 | (e^h - 1) / h ≈ 0.010050166
h= 0.001 | (e^h - 1) / h ≈ 0.001000500
h= 0.0001| (e^h - 1) / h ≈ 0.000100005
As h approaches 0, we can see that the values of the expression get closer and closer to the value 1. Hence, we can estimate that the limit is equal to 1:
lim (e^h - 1) / h ≈ 1, as h approaches 0.
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