H-x-8-x-2-and-f-x-x-2-3x-6-2x-4-1-Calculate-the-surface-V-n-of-area-limited-by-the-the-line-x-6-x-6-n-n-N-and-the-curve-of-H-x-and-f-x-in-function-of-n-2-Knowing-that-1-2-2-2-

Question Number 137321 by mathocean1 last updated on 01/Apr/21

H (x) = \frac{8}{x - 2} a n d f (x) = \frac{x^{2} + 3 x + 6}{2 x - 4}

1) C a l c u l a t e t h e s u r f a c e V_{\boldsymbol n} o f

a r e a l i m i t e d b y t h e t h e l i n e

x = 6; x = 6 + \boldsymbol n (n \in N^{*}) a n d t h e

c u r v e o f H (x) a n d f (x) i n f u n c t i o n

o f \boldsymbol n .

2) K n o w i n g t h a t 1^{2} + 2^{2} + \dots + n^{2} = \frac{n (n + 1) (2 n + 1)}{6}

D e d u c t t h e v a l u e o f

S_{n} = V_{1} + V_{2} + \dots + V_{n} i n f u n t i o n

o f n .

3) D e t e r m i n a t e t h e s m a l l e s t

i n t e g e r n s u c h t h a t S_{n} > 100