Question Number 149329 by mnjuly1970 last updated on 04/Aug/21
Commented byKamel last updated on 04/Aug/21
![I think I^(100) +k≡0[14]](Q149366.png)
Answered by Kamel last updated on 04/Aug/21
![∫_0 ^(π/2) ((e^(−tan(x)) sin^2 (x))/(cos^6 (x)))dx=^(t=tan(x)) ∫_0 ^(+∞) (t^2 +t^4 )e^(−t) dt=2+4!=26 26^(100) +k≡0[14] 26≡−2[14]⇒26^(100) ≡2^(100) [14] 2^4 ≡2[14]⇒2^(100) ≡2^(25) [14]⇒2^(100) ≡2^(10) [14]⇒2^(100) ≡2[14] ∴ k≡−26^(100) [14]⇒k≡−2[14]⇒k≡12[14] ∴ k=14n+12⇒k_(min) =12, k>0.](Q149365.png)
Commented bymnjuly1970 last updated on 05/Aug/21
Question Number 149329 by mnjuly1970 last updated on 04/Aug/21 | ||
| ||
Commented byKamel last updated on 04/Aug/21 | ||
| ||
Answered by Kamel last updated on 04/Aug/21 | ||
| ||
Commented bymnjuly1970 last updated on 05/Aug/21 | ||
| ||