You are here:

Calculus/bunch of Qz involving limitz

Advertisement

Expert: Alon Mandes - 1/9/2010


Question
hello
1)is Lim e^(x-x^2) as x approaches infinity =0 ????

2)just to make sure, there is no vertical asympototes to:
y=(square root of(x^2+x+1)-square root of(x^2-x) ???

3) find the vertical asympototes of :
y=tan(2sin(x)) in the closed intervel {-PI,PI} ???

4)if Lim f(x)/x^(2) equels 5
find Lim f(x)/x as x approaches zero? is at 5 as well ????  

Answer
Hi Nora,
1) Lim e^(x-x^2) = 0 ("because x-x^2 is negative for all x>1")
  x->INF
2) y=(square root of(x^2+x+1)-square root of(x^2-x) Has no verical asymptote
3) y=tang[2sin(x)]. The tangent function has a vertical asymptotes at pi/2 . Therefore,
  2sin(x)=pi/2 --> sin(x)=pi/4 --> x=51.75 degrees = 0.9 radian . ("since sin & tan are
  odd functions , the answer will be +0.9 & -0.9 ")
4) Lim   f(x)/x^2=5
  x->0    
  Lim   f(x)/x = Lim  xf(x)/x^2 = Lim  x[f(x)/x^2)] = Lim  x*g(x) = 0
  x->0           x->0             x->0                x->0
  Because g(x) is bounded . An example for this : take f(x)=5x^2 .

Alon.

Calculus

All Answers

Answers by Expert:

Ask Experts

Volunteer

Alon Mandes

Expertise

Kind of questions I can answer : Limits, Derivatives, Integration, Implicit functions, continuousity, differentiation ,Extremum problems, Lagrange multipliers, Gradients, Surface integrals, Multi variables functions ,Multi variables Integrals,Complex variables ,Complex functions, Curves, Trajectory integrals & Vector analyse,Divergence,Rotor & word problems. Kind of question I can't answer : Economics,Combinatorics,infinite series & convergence ,Statistics & Probabilities .

Experience

1. I'm a team member of mathnerds (math site for answering questions) 2. I'm a team member in the Student's Union of the Technion, helping students who have problems in mathematics. 3. 2 years of experience as a math teacher in college. 4. I give free homework help for high school students in Mathematics & Physics. 5. I teach part time in collage the subjects : "Digital Signal Processing" , "Random Signals & Noise" , "Complex Functions".

Organizations
Hi-Tech company : GSM4VOIP ; job possition : Algorythm developer.

Education/Credentials
M.A in Mathematics & Bs.c in Electronics.

©2012 About.com, a part of The New York Times Company. All rights reserved.