Question

Use a calculator to estimate the values of the limits correctly to two decimal places.

*h is approaching 0 in both of these limits

`\lim_(h \to \0) (2.7^h-1)/(h) \\\\ \lim_(h \to \0) (2.8^h-1)/(h)`

Answer 1

Try this option ↓

Explanation:

1) if to evaluate the given limits using math methods, then:

`\lim_(h \to 0) (2.7^h-1)/(h)=[(0)/(0)]= \lim_(h \to 0) ((2.7^h-1)')/((h)')= \lim_(h \to 0) (2.7^h*ln2.7)/(1) =ln2.7;`

and

`\lim_(h \to 0) (2.8^h-1)/(h)=[(0)/(0)]= \lim_(h \to 0) ((2.8^h-1)')/((h)')= \lim_(h \to 0) (2.8^h*ln2.8)/(1) =ln2.8;`

2) for more info see the attached graphs; note, ln2.7≈0.993252, ln2.8≈1.029619 and the function is undefined in the points where x=0.