Question

Find a reasonable estimate of the limit 649-15-01-00-00_files/i0140000
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Answer 1

Choice C is the correct answer

Explanation:

Direct substitution of the limit into the expression yields;

`(2^(5)-32 )/(2^(3) -8) =(0)/(0)`

which represents an indeterminate form.

We therefore apply L'Hospitals rule to evaluate the limit;

We differentiate the numerator and the denominator separately, simplify the resulting expression and finally substitute the limit;

Differentiating the numerator and the denominator yields;

`(5x^(4) )/(3x^(2) ) =(5)/(3) x^(2)`

Substituting x =2 into the last expression yields;

`(5)/(3) *2^(2) =(20)/(3)=6.6667`