Question

lim x->0 ((1+x)/(2+x))*(1-x^1/2)/(1-x)
can I just put 0 inside and get: 1/2
or there is something tricky here?

Answer 1

U can Just Put 0 inside :)

Answer 2

1/2*1/2 = 1/4 u should get

Answer 3

I don't see anything preventing you from doing that, so yeah.

Answer 4

@ganibl It should be 1/2, the second part should yield 1/1 instead of 1/2

Answer 5

opops sorry my bad

Answer 6

so, it's 1/2, thank you!

Answer 7

now I see what's the point of the question: the next one is the same but x->1
And now it will be impossible to just insert 0.

Answer 8

It's only necessary to do something "tricky", as you call it, if you get either something over 0 or an indeterminate form (like 0/0, 1^infinity, stuff like that)

Answer 9

Well, actually, probably not even something over 0. I forgot his is already calculus.

Answer 10

now I will need to use the principle with e?

Answer 11

Easiest way I can think of is multiply them together first then apply l'hopital's rule. Not entirely sure if this will get you something workable, though

Answer 12

I don't know l'hopital's rule, unfortunately.

Answer 13

I mean, I am supposed to get the result using something else.

Answer 14

Was that not part of your curriculum?

Answer 15

no

Answer 16

Ah, I see. In that case, I need to look at it some more

Answer 17

Just to be clear, is the question supposed to say 1-x^1/2 or (1-x)^1/2?

Answer 18

1-x^1/2

Answer 19

2+x/2+x + (-1)/2+x ?

Answer 20

Multiply the second part by (1+x^1/2)/(1+x^1/2), you should be able to get rid of 1-x terms

Answer 21

still got stuck...

Answer 22

Working with the second part:
(1-x^1/2)/(1/x)
=((1-x^1/2)/(1/x))*((1+x^1/2)/(1+x^1/2))
=((1-x^1/2)(1+x^1/2))/((1-x)(1+x^1/2))
=(1-x)/((1-x)(1+x/^1/2))
=1/(1+x^1/2)

Answer 23

After which there is nothing stopping you from substituting x=1 in.

Answer 24

got it! thanks!