Take the ratio of the derivatives of numerator and denominator, and evaluate it at the x value in question.
For both problems, the derivative of the denominator is just 1, so you just have to evaluate the derivative of the numerator.
In the first problem,
Lim [�ã(x + 1)-(2)]/(x-3)
x -> 3
= (1/2�ã(x + 1)
= 1/4 at x =3
For the second problem
Lim [(1/(x+4)-(1/4)]/ x
x -> 0
= -1(x+4)^2 at x=0
= -1/16
1.) Lim [√(x + 1) - (2)] / (x - 3)
x -> 3
2.) Lim [ (1/ x + 4) - (1 / 4)] / (x)
x -> 0
1 answer