Question Number 71360 by 20190927 last updated on 14/Oct/19

lim_(x→0) ((1−(√(1+2x^4 ))cos ((√2)x^2 ))/(x^5 ln (1−2x^3 )))

Commented bymathmax by abdo last updated on 14/Oct/19

for x∈ V(0) (√(1+2x^4 )) ∼1+x^4 and cos((√2)x^2 )∼1−((2x^4 )/2) =1−x^4 ⇒ 1−(√(1+2x^4 )) cos((√2)x^2 )∼1−(1+x^4 )(1−x^4 )=1−(1−x^8 ) =x^8 ln(1−2x^3 ) ∼−2x^3 ⇒x^5 ln(1−2x^3 )∼−2x^8 ⇒ lim_(x→0) ((1−(√(1+2x^4 ))cos((√2)x^2 ))/(x^5 ln(1−2x^3 ))) =−(1/2)

Commented by20190927 last updated on 17/Oct/19

thanks