Use L'Hospital's Rule to find limit

[andrey21]

Use L'Hospital's rule to find the limit of the following:

(SQRT (3+x) -2)/(x-1)

As x tends to 1



Here's my attempt

Let f(x) = SQRT(3+x) - 2 g(x) = x-1

f'(x) = 1/2 (SQRT(3+x)) g'(x) = 1


Therefore f'(x)/g'(x) is:


1/2(SQRT(3+x)/1

=1/2(SQRT(3+1)
= 1/2(SQRT(4))

=1/4

 

[andrey21]

Please any comments would be greatly appreciated.

 

[Mark44]

Looks good.

 

[andrey21]

Thank you Mark 44