Use L'Hopital's rule and take the ratio of the derivatives of numerator and denominator.
The derivative of the numerator at x = 7 is
(9/2)/(9x+5)^(1/2)= (9/2)/sqrt68 = 0.5457..
and the derivative of the denominator is 1.
Therefore your answer is correct. If you want the exact value, use
(9/2)/sqrt68
(sqrt(9x+5)-sqrt(68))/(x-7) limit as x approaches 7
the answer i got was .0546 i am not sure if this is right also, if it is ...is there a more exact fraction .... like if the answer was 0.3333333 a better way to write it would be 1/3
4 answers
Thank you so much!!
Actually, your answer is ten times too low. Did you slip a decimal point somewhere?
i accidentally put the 0 in the wrong place in the above response i had 0.546...