How do you solve this derivative?

Question

lim [(1 + x^1/2)/(2 + x^1/2)] =
x=>00


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possible solutions given from book.....


a. 0

b. 1/2

c. 1

d. e^3

e. 3e

f. 2

g. - oo

h. oo

or is it none of these ?

Answer 1

That is not a derivative. That is a limit, and it's completely unnecessary to use derivatives to solve it. Consider the following:

[x→∞]lim (1 + √x)/(2 + √x)
[x→∞]lim (2+√x)/(2+√x) - 1/(2+√x)
[x→∞]lim 1 - 1/(2+√x)

Evaluating the limit, we see that the second fraction is of the form 1/∞, which goes to zero. Therefore, the limit is 1-0 or simply 1.