calculus
posted by thomas .
just wondering if someoen could help me with this limit..:
lim arctan[(x^2  4)/(3x^26x)]
x>2

My first step in doing limits is to sub in the approach value, this will give me Lim arctan (0/0)
This just about guarantees that the algebraic expression will factor and the offending factor will cancel.
Sure enough
lim arctan[(x^2  4)/(3x^26x)] x>2
= lim arctan[(x+2)(x2)]/[3x(x2)]
=lim arctan[(x+2)]/[3x]
= lim arctan(2/3)
now use your calculator, set to radian mode, to find
lim arctan[(x^2  4)/(3x^26x)] x>2
= .588 
thanks for the reply... the question asks me to evaluate the limit using continuity, how do i justify my answer with continuity?
Respond to this Question
Similar Questions

limiting position of the particle
A particle moves along the x axis so that its position at any time t>= 0 is given by x = arctan t What is the limiting position of the particle as t approaches infinity? 
Calculus
Note that pi lim arctan(x ) =  x > +oo 2 Now evaluate / pi \ lim arctan(x )   x x > +oo \ 2 / I'm not exactly sure how to attempt it. I have tried h'opital's rule but I don't believe you can use it here. Any help … 
calculus again
Suppose lim x>0 {g(x)g(0)} / x = 1. It follows necesarily that a. g is not defined at x=0 b. the limit of g(x) as x approaches equals 1 c.g is not continuous at x=0 d.g'(0) = 1 The answer is d, can someone please explain how? 
Calculus
Show that limit as n approaches infinity of (1+x/n)^n=e^x for any x>0... Should i use the formula e= lim as x>0 (1+x)^(1/x) or e= lim as x>infinity (1+1/n)^n Am i able to substitute in x/n for x? 
Calculus
Show that limit as n approaches infinity of (1+x/n)^n=e^x for any x>0... Should i use the formula e= lim as x>0 (1+x)^(1/x) or e= lim as x>infinity (1+1/n)^n Am i able to substitute in x/n for x? 
calculus
lim (x^31)/(x^3+2x^2y+xy^2x^22xyy^2) (x,y)>(1,0) my question is can you approach (1,0) with y=x and does that change the the limit to lim f(x,x) (x,x)>(1,1) in which case i get 3/4 as the limit. and if this is not how i … 
Calculus
I am maybe overthinking this, but what is the lim as n> infinity of (n+1)/(n+2) ? 
Calculus. Limits. Check my answers, please! :)
4. lim (tanx)= x>pi/3 (sqrt3) 1 (sqrt3) ***1 The limit does not exist. 5. lim x= x>2 2 ***2 0 1 The limit does not exist. 6. lim [[x]]= x>9/2 (Remember that [[x]] represents the greatest integer function of x.) 4 … 
Calculus
Find the limit. lim 5x/(x^225) x>5 Here is the work I have so far: lim 5x/(x^225) = lim 5x/(x5)(x+5) x>5 x>5 lim (1/x+5) = lim 1/10 x>5 x>5 I just wanted to double check with someone and see if the answer … 
Calculus (lim)
consider the statement lim x³6x²+11x6 / x1 = 2 x>1 Using the definition of the limit, state what must be true for the above limit to hold, that is, for every ..., there is ..., so that.... Use a specific function and limit …