Question

सीमाओं के मान प्राप्त कीजिए : $\lim_{x\rightarrow3}\dfrac{x^4 - 81}{2x^2 - 5x - 3}$

Answer 1

Answer:

$\large\boxed{\sf{\dfrac{108}{7}}}$

Step-by-step explanation:

$\lim_{x\rightarrow3} \frac{ {x}^{4} - 81 }{2{ x }^{2} - 5x - 3} \\ \\ = \lim_{x\rightarrow3} \frac{ {( {x}^{2} )}^{2} - {9}^{2} }{2 {x}^{2} - 6x + x - 3} \\ \\ = \lim_{x\rightarrow3} \frac{( {x}^{2} + 9)( {x}^{2} - {3}^{2}) }{2x(x - 3) + 1(x - 3)} \\ \\ = \lim_{x\rightarrow3} \frac{ {(x}^{2} + 9)(x + 3)(x - 3) }{(2x + 1)(x - 3)} \\ \\ = \lim_{x\rightarrow3} \frac{( {x}^{2} + 9)(x + 3)}{(2x + 1)} \\ \\ = \frac{( {3}^{2} + 9)(3 + 3)}{(2 \times 3) + 1} \\ \\ = \frac{(9 + 9) \times 6}{6 + 1} \\ \\ = \frac{18 \times 6}{7} \\ \\ = \frac{108}{7}$

Answer 2

108/7    $\lim_{x\rightarrow3}\dfrac{x^4 - 81}{2x^2 - 5x - 3} = \frac{108}{7}$

Step-by-step explanation:

$\lim_{x\rightarrow3}\dfrac{x^4 - 81}{2x^2 - 5x - 3}$

x = 3  प्रयोग करने पर  

= (3⁴  -81)/(2(3)² - 5(3) - 3)

= 0/0

परिभाषित नहीं

x⁴ - 81

= (x²)²  - 9²

= (x² + 9)(x² - 9)

= (x² + 9)(x + 3)(x - 3)

2x² - 5x - 3

= 2x² - 6x + x - 3

= 2x(x - 3) + 1(x - 3)

= (2x + 1)(x - 3)

(x² + 9)(x + 3)(x - 3) /  (2x + 1)(x - 3)

=  (x² + 9)(x + 3)/(2x + 1)

x = 3  प्रयोग करने पर  

=   (3² + 9)(3 + 3)/(2*3 + 1)

= 18*6/7

= 108/7

$\lim_{x\rightarrow3}\dfrac{x^4 - 81}{2x^2 - 5x - 3} = \frac{108}{7}$

और पढ़ें

सीमाओं के मान प्राप्त कीजिए :  [tex]\lim_{x\rightarrow3}\dfrac{x^4 - 81

https://brainly.in/question/15778085

सीमाओं के मान प्राप्त कीजिए

https://brainly.in/question/15778083