Calc
posted by Urgent .
I have a test soon.. and I really need to know how to do this problem.. please help!!!
lim as x>0 sin^2(x)/tan(x^2)
the answer is 1, but I have no clue how to get that!
Use series expansions. Look up Taylor expansion on google and study that topic first.
Using series expansion techniques these limit problems become pretty trivial. For x in a neighborhood of zero:
Sin(x) = x + O(x^3) >
sin^2(x) = x^2 + O(x^4)
tan(x) = x + O(x^3) >
tan(x^2) = x^2 + O(x^6)
And you see that:
sin^2(x)/tan(x^2) = 1 + O(x^4)
So, the limit is 1
Respond to this Question
Similar Questions

Maths complex numbers
Find tan(3 theta) in terms of tan theta Use the formula tan (a + b) = (tan a + tan b)/[1  tan a tan b) in two steps. First, let a = b = theta and get a formula for tan (2 theta). tan (2 theta) = 2 tan theta/[(1  tan theta)^2] Then … 
CalculusLimits
Okay, i posted this question yesterday, however, I did not really understand the answer I received. If your the one who answered my question, could you please elaborate. If not, could you try to answer this tough, for me, question. … 
CALCULUS  need help!
Determine the limit of the trigonometric function (if it exists). 1. lim sin x / 5x (x > 0) 2. lim tan^2x / x (x >0) 3. lim cos x tan x / x (x > 0) 
Calculus
Below are the 5 problems which I had trouble in. I can't seem to get the answer in the back of the book. Thanks for the help! lim (thetapi/2)sec(theta) theta>pi/2 Answer: 1 I am not sure what to do here. lim (tan(theta))^(theta) … 
Math  help really needed
Prove each idenity. 1+1/tan^2x=1/sin^2x 1/cosxcosx=sinxtanx 1/sin^2x+1/cos^2x=1/sin^2xcos^2x 1/1cos^2x+/1+cosx=2/sin^2x and (1cos^2x)(1+1/tan^2x)= 1 I haven't even gotten 'round to sny of the quedtions because the first one is just … 
Math  help really needed
I'm sorry to double post; I don't want to seem impatient, but I really need help with this. Prove each idenity. 1+1/tan^2x=1/sin^2x 1/cosxcosx=sinxtanx 1/sin^2x+1/cos^2x=1/sin^2xcos^2x 1/1cos^2x+/1+cosx=2/sin^2x and (1cos^2x)(1+1/tan^2x)= … 
calc bc (condensed
is the limit as x approaches 0 of sin3x over 3x equal to zero? 
Calc
Use a table of values to estimate the value of the limit. lim (tan 3x/tan 5x) x> 0 I have no clue what to do. Could someone please explain how to go about this problem. 
calculus
f(x)= 3x+2, x<0 3, x=0 x^2+1, x>0 g(x)= x+3, x<1 0, x=1 x^2, x>1 find a) lim x>0+ g(f(x)) b)lim x>0 g(f(x)) c) lim x>1+ f(g(x)) d)lim x>1 f(g(x)) I am trying to understand these. Help appreciated. Have … 
Pre calc
Find sin(2x), cos(2x), and tan(2x) from the given information. sin(x) = 5/13, x in Quadrant I sin(2x)?