+0

# Kevin Zhang HMU / lim as x approaches 1 (x^(1/m)-1)/(x^(1/n)-1)

0
655
1

UH82CIT

lim as x approaches 1 (x^(1/m)-1)/(x^(1/n)-1)

Guest Apr 1, 2015

#1
+26625
+5

Let x = 1 + δ, where δ is very small and tends to zero as x tends to 1.

Then x1/m = (1 + δ)1/m → 1 + δ/m as δ → 0

Simnilarly x1/n → 1 + δ/n

This means (x1/m -1)/(x1/n - 1) → (1 + δ/m - 1)/(1 + δ/n - 1) → (δ/m)/(δ/n) → n/m

So the limit of (x1/m -1)/(x1/n - 1) as x → 1 is n/m

.

Alan  Apr 2, 2015
Sort:

#1
+26625
+5

Let x = 1 + δ, where δ is very small and tends to zero as x tends to 1.

Then x1/m = (1 + δ)1/m → 1 + δ/m as δ → 0

Simnilarly x1/n → 1 + δ/n

This means (x1/m -1)/(x1/n - 1) → (1 + δ/m - 1)/(1 + δ/n - 1) → (δ/m)/(δ/n) → n/m

So the limit of (x1/m -1)/(x1/n - 1) as x → 1 is n/m

.

Alan  Apr 2, 2015

### 20 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details