Evaluate the following. 106 A. 60 B. 100,000 C. 10,000 D. 1,000,000
2 answers:
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Answer:
Step-by-step explanation:
we would like to compute the following limit:
if we substitute 0 directly we would end up with:
which is an indeterminate form! therefore we need an alternate way to compute the limit to do so simplify the expression and that yields:
now notice that after simplifying we ended up with a<em> </em><em>rational</em><em> </em>expression in that case to compute the limit we can consider using L'hopital rule which states that
thus apply L'hopital rule which yields:
use difference and Product derivation rule to differentiate the numerator and the denominator respectively which yields:
simplify which yields:
unfortunately! it's still an indeterminate form if we substitute 0 for x therefore apply L'hopital rule once again which yields:
use difference and sum derivation rule to differentiate the numerator and the denominator respectively and that is yields:
thank god! now it's not an indeterminate form if we substitute 0 for x thus do so which yields:
simplify which yields:
finally, we are done!
