Question

lim {√(1+x) - √x} Ln 1/x​

Answer 1

Answer:

infinity

Step-by-step explanation:

sqrt(1+x)-sqrt(x)=

multiply and divide with sqrt(1+x) + sqrt x

( sqrt(1+x)-sqrt x ) × (sqrt(1+x) + sqrtx)

____________________________

sqrt(1+x) + sqrt x

1+x-x 1

= _____________ = ____________

sqrt(1+x) + sqrt x sqrt(1+x)+sqrt x

lim ln1/x ÷ sqrt(1+x)+sqrt x

x ‐> infinity

it is in form infinity /infinity

as lim lnx = - infinity

x->0

use l hospital rule

lim f(x)/g(x) = lim f'(x)/g'(x)

x->c x->c

let f(x)=ln1/x,

let g(x)=sqrt(1+x)+sqrt x

f'(x)= 1/(1/x)=x

g'(x)= 1/(2×(1+x)½) + 1/2x½

lim f'(x) = infinity

x->infinity

lim g'(x) = 0+0=0

x->infinity

lim f'(x)/g'(x) =infinity/ 0=infinity

x -> infinity

tried my best to answer, hope it is helpful