## pasta 3 years ago find the lim (x+1/x) as x tends to 0.and sketch a graph to support for answer.

1. 2le

$lim_{x \rightarrow 0}(x+\frac{1}{x})=lim_{x \rightarrow 0}(\frac{x^2+1}{x})$ From here you can see that the function gets larger and larger as x approaches 0 from the left and the right.|dw:1349841452926:dw| also, if you look at $lim_{x \rightarrow \infty}(\frac{x^2+1}{x})=2$ $lim_{x \rightarrow -\infty}(\frac{x^2+1}{x})=2$from l'Hopital's rule

2. pasta

as x tends to infinity the function is undefined as far as i know

use l'hopital rule

|dw:1350219305254:dw|

then the x^2 cancels out.....the eq left is 1/x^2...... now when x approaches 0 the eq. approaches infinity,...!!1 so infinity is the ans

graph is this and its correct

|dw:1350219633729:dw|

range of the grph is (-infinity , -2] union [2,infinity)

9. pasta

@adi171 there is no way i can use l 'HOpitals rule becoz the function gives 1/0 not 0/0 OR infnty/infnty.

10. pasta

when i use the rule my derivative is 2x which gives the answer 0.HOW ARE YOU differentiating 2x/1 which is actualy the derivative .and it does not work for the rule on this case

11. pasta

you are finding the minimum and maximum points of this graph. as x tends to inifinity the function tends to infinity .and AS X tends to 0 the function is undefined(see the attached graph)