Asked by MW
lim x approaches 0
[1/x *((1/(sqrt(1+x))-1)]
It will be easier to understand if you write it out..
How would I algebraically do this? (The answer is -1/2)
Help please?
[1/x *((1/(sqrt(1+x))-1)]
It will be easier to understand if you write it out..
How would I algebraically do this? (The answer is -1/2)
Help please?
Answers
Answered by
drwls
I suggest you use L'Hopital's rule. The limit of the ratio of (1/(sqrt(1+x))-1)] to x is the ratio of the derivatives of numerator and denominator.
The derivative of x (the denominator) is 1.
The derivative of 1/(sqrt(1+x) -1 at x = 0 is (-1/2)(1+x)^-3/2 = -1/2
So the limit is (-1/2)/1 = -1/2
The derivative of x (the denominator) is 1.
The derivative of 1/(sqrt(1+x) -1 at x = 0 is (-1/2)(1+x)^-3/2 = -1/2
So the limit is (-1/2)/1 = -1/2
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