Find the Limit of: Lim h-->1 of (1-(1/h^2)) / (1-(1/h))?

Question

show work please

Answer 1

I just did this. the function Simplifies to (x+1)/x

so it is just (1+1)/1=2

Answer 2

Make the substitution 1/h = a, so the limit becomes:

lim (1-a)(1+a)/(1-a)
a->1

lim (1+a) = 2
a->1

Answer 3

L'Hospital rule

Lim = d/dx (1-1/h^2) / d/dx (1-1/h)
h ->1

Lim = d/dx (1-h^-2) / d.dx (1 - h^-1)
h -> 1

Lim = 2h^-3 / h^-2
h-> 1

Lim = (2/h^3) / (1/h^2)
h -> 1

Lim = 2/h^3 * h^2
h -> 1

Lim = 2/h
h -> 1

now plug 1 in for h
lim = 2/1
lim = 2 <== answer
h -> 1

Answer 4

[1- (1/h^2)/(1-(1/h)

=>[(1+(1/h))(1-(1/h)]/[(1-(1/h))]

=>(1+(1/h))

when h -> 1 , the expression becomes

(1+(1/1)) = 1+1 = 2