Question

Need solution..................

Answer 1

$Given : \lim_{2} \frac{x^3 - 8}{x^4 - 16}$

$\lim_{2} \frac{(x-2)(x^2 + 2x + 4)}{(x + 2)(x - 2)(x^2 + 4)}$

$\lim_{2} \frac{x^2+2x+4}{(x+2)(x^2+4)}$

$\frac{2^2 + 2(2) + 4}{(2 + 2) * (2^2 + 4)}$

$\frac{4 + 4 + 4}{(4)(4 + 4) }$

$\frac{12}{32}$

$\frac{3}{8}$



Hope this helps!

Answer 2

We can  apply L'Hospital Rule When the indeterminate expression  is the form of  0/0 or ∞/∞

[To find the limits of other indeterminate forms we try to convert each form to 
 0/0 or ∞/∞ and apply L'Hospital rule]

See the IMAGE: FOR SOLUTION

THE ANSWER IS 3/8.

We  differentiate the NUMERATOR And DENOMINATOR separately