Question

Please help me find limit​

Answer 1

9514 1404 393

Answer:

-13/11

Explanation:

Straightforward evaluation of the expression at x=1 gives (1 -1)/(1 -1) = 0/0, an indeterminate form. So, L'Hopital's rule applies. The ratio of derivatives is ...

`\displaystyle\lim_(x\to 1)(n)/(d)=(n')/(d')=\left.\frac{\frac{4}{3\sqrt[3]{4x-3}}-(7)/(2√(7x-6))}{(5)/(2√(5x-4))-\frac{2}{3\sqrt[3]{2x-1}}}\right|_(x=1)=(4/3-7/2)/(5/2-2/3)=(8-21)/(15-4)\\\\=\boxed{-(13)/(11)}`