Question

evaluate lim X-->5(x⁴-625÷X-5)​

Answer 1

Answer:

see the attached document

Answer 2

Answer:

The value of  $\lim_{x \to 5} (\frac{x^{4}-625 }{x-5} )$ = 500.

Step-by-step explanation:

Given that lim x-->5(x⁴-625÷x-5)

We have to simplify the above expression

$\lim_{x \to 5} (\frac{x^{4}-625 }{x-5} )$

$= \lim_{x \to5} (\frac{x^{4}-5^{4} }{x-5} )$      

since 5×5×5×5= 25×25 = 625

(a + b)(a - b) = a² -b²

Applying above formula in the given expression

$\lim_{x \to 5} (\frac{x^{4}-625 }{x-5} )$

$= \lim_{x \to5} (\frac{x^{4}-5^{4} }{x-5} )$  

$= \lim_{x \to5} \frac{ (x^{2} +5^{2} )(x^{2} -5^{2}) }{x-5}$

Here again applying (a + b)(a - b) = a² - b²

$= \lim_{x \to5} \frac{(x^{2} +5^{2})(x+5)(x-5) }{x-5}$

$= \lim_{x \to 5}(x^{2} +25)(x+5)$

$= (5^{2} +25)(5+5)$

= (25+25)(10)

=50 × 10

=500

Therefore, the value is 500.