Math, asked by kardiles583, 29 days ago

evaluate lim X-->5(x⁴-625÷X-5)​

Answers

Answered by sumanhalder08
9

Answer:

see the attached document

Attachments:
Answered by visalavlm
10

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.

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