Answer:
Choice C is the correct answer
Step-by-step explanation:
Direct substitution of the limit into the expression yields;
[tex]\frac{2^{5}-32 }{2^{3} -8} =\frac{0}{0}[/tex]
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;
[tex]\frac{5x^{4} }{3x^{2} } =\frac{5}{3} x^{2}[/tex]
Substituting x =2 into the last expression yields;
[tex]\frac{5}{3} *2^{2} =\frac{20}{3}=6.6667[/tex]
