Menu Close

lim-x-0-x-x-x-1-1-4-1-




Question Number 131882 by Eric002 last updated on 09/Feb/21
lim_(x→0)  (x/(x+((x+1))^(1/4) −1))
limx0xx+x+141
Answered by liberty last updated on 09/Feb/21
 L′Ho^  pital L= lim_(x→0)  [ (1/(1+(1/(4 (((x+1)^3 ))^(1/4) )))) ]=(1/(1+(1/4)))= (4/5)  or lim_(x→0) [ (x/(x+1+(x/4)−1))] = lim_(x→0)  ((4x)/(5x))=(4/5)
LHopital¨L=limx0[11+14(x+1)34]=11+14=45orlimx0[xx+1+x41]=limx04x5x=45
Commented by Eric002 last updated on 09/Feb/21
how did you get (x/(x+1+(x/4)−1))
howdidyougetxx+1+x41
Commented by EDWIN88 last updated on 09/Feb/21
Bernoulli equation    lim_(x→0)  (1+f(x))^n  ≈ lim_(x→0) (1+n.f(x))   so lim_(x→0)  ((1+x))^(1/4)  ≈ lim_(x→0)  (1+(x/4))
Bernoulliequationlimx0(1+f(x))nlimx0(1+n.f(x))solimx01+x4limx0(1+x4)
Commented by Eric002 last updated on 09/Feb/21
thank you sir
thankyousir
Answered by EDWIN88 last updated on 09/Feb/21
the another way   let ((x+1))^(1/4)  = ℓ where ℓ→1 and x=ℓ^4 −1  L=lim_(ℓ→1)  ((ℓ^4 −1)/(ℓ^4 +ℓ−2)) = lim_(ℓ→1)  (((ℓ^2 +1)(ℓ+1)(ℓ−1))/((ℓ−1)(ℓ^3 +ℓ^2 +ℓ+2)))    = lim_(ℓ→1)  (((ℓ^2 +1)(ℓ+1))/(ℓ^3 +ℓ^2 +ℓ+2)) = (4/5)
theanotherwayletx+14=where1andx=41L=lim1414+2=lim1(2+1)(+1)(1)(1)(3+2++2)=lim1(2+1)(+1)3+2++2=45
Answered by mathmax by abdo last updated on 10/Feb/21
let f(x)=(x/(x+^4 (√(1+x))−1)) ⇒f(x)=(x/(x+(1+x)^(1/4) −1))  ⇒f(x)∼(x/(x+1+(x/4)−1))=(x/((5/4)x))=(4/5) ⇒lim_(x⌣)0)   f(x)=(4/5)
letf(x)=xx+41+x1f(x)=xx+(1+x)141f(x)xx+1+x41=x54x=45limx)0f(x)=45

Leave a Reply

Your email address will not be published. Required fields are marked *