1) I always try to avoid any problem involving Sin(x)/x I do not know what exactly to do I get confused to where am I supossed to plug in the limit especially when it is zero
2) The other types of problems that I have trouble with are the problems with fractions in fractions. For instance, [(1/x+1)+(1/2x)]/x these types of problems get me stumble because I forget how to simplify the problem. Then the same thing about plugging in the limit especially when it is zero...damn zeroes.
3) Int type problems just stumble me. I know how they look but I can't graph them without using the calculator and I really do not know how to find the limit at all I try but fail HELP!!!
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ok for number 1, sinx / x is equal to 1 when the limit is a number. when the limit involves + or - infinity sinx / x equals 0 i think.
ReplyDeletei know it doesnt really help when i dont know for sure but hopefully im helping you out a little or creating a brainstorm
Concept #1 - You plug in the approaching number when the function is simplified all the way like x+3 in order to find the limit.
ReplyDeleteConcept #2 - Memorize this.
The limit of Sin(x)/x when x approaches positive or negative infinity is 0.
The limit of Sin(x)/x when x approaches 0 is 1.
When you got this down, you can replace any sin(x)/x with 0 or 1 depending on whether if x is approaching positive or negative infinity or 0.
Concept #3 - Take things down one step at a time. When simplifying a fraction within a fraction start with the numerator. Expand the numerator (so that you can see it better) and add like terms. Once you got that down, go to the denominator and add like terms. Now place what you got on the numerator on top and what you got on the denominator on the bottom. And that is your simplified function.
Concept #4 - After simplifying the equation to the point you cant simplify anymore and if you still plug in 0 for x and still get 0 for the denominator then the limit of that function does not exist.
Responding to Krystal, the limit is only 1 when x approaches 0, not just any constant. For sinx / x, you really only have to memorize the two limits, when x approaches infinity and when x approaches 0.
ReplyDeleteAs for intx, the function INT simply rounds DOWN to the nearest integer (+/-whole numbers). Choose random numbers for x, including fractions/decimals and see what you output is. You really only have to do it carefully once and you'll get the hang of it. If you have the graph, can you find the limit?
hey YEAH i was rite then,,sin(x) as it approaches infinity it's 0 but,,sttill WHYY??? IF IT DOESNTTTT get to close to zero. I feel it'll look that way if the x it's divided by a fraction. :s
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