Question

lim x tend 0 root x+7-root7/x​

Answer 1

Step-by-step explanation:

Lim x -> 0 {√(x + 7) - (√7)} / x

0/0 form then use D-L hospitalization rule :

Lim x -> 0 {√(x + 7) - (√7)} / x

according to D-L hospitalization rule :

Lim x-> 0 f(x)/g(x) = f'(0)/g'(0) = df(x)/dx / dg(x)/dx

so now solve given question :

Lim x -> 0 {√(x + 7) - (√7)} / x

= {(x+7)^1/2 - 7^1/2} / x

= {(1/2)×(x+7)^-1/2 - 0} / 1

put limit x -> 0

= (1/2)*(7)^-1/2

= (1/2)(1/√7)

= 1/2√7