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!
First we define the variables:
m = multiple choice questions
s = short answer questions
Next we need to satisfy 2 conditions:
1) There are a total of 40 questions. We can represent this mathematically using the variables I defined:
2) The multiple-choice questions are worth 2 points and the short-answer are worth 4 points but they need to total 100 points. This can also be represented mathematically:
By satisfying the conditions provided we were able to create the 2 equations!
Answer:
Step-by-step explanation: