Please find the result !​

Step-by-step explanation:

we would like to compute the following limit:

if we substitute 0 directly we would end up with:

which is indeterminate! therefore we need 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 rational 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 indeterminate 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 indeterminate if we substitute 0 for x thus do so which yields:

simplify which yields:

finally, we are done!

0,0

step-by-step explanation:

the ratios are reciprocals im positive

step-by-step explanation:

they are all positive numbers so it wouldn't be the other ones