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zell_D
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lim x->0 3sin4x/sin3x i do not know how to reduce the sin4x? and do i even use the property where lim x->0 sinx/x =1?
no, there's an identity that's probably on the inside cover of your textbook. it goes something like sin(a+b) = cos(a)sin(b) + cos(b)sin(a). i can't remember how that formula goes but it's something like that.zell_D said:ok thanks another REAL DUMB question on my part lol haven't done math for so long, when i make sin4x into sin2(2x) and then into 2sin2xcos2x, do i use distributive property with the 3?
The suggestions so far would work, but are not the best way.zell_D said:lim x->0 3sin4x/sin3x i do not know how to reduce the sin4x? and do i even use the property where lim x->0 sinx/x =1?
Pretty clever.lurflurf said:The suggestions so far would work, but are not the best way.
[tex]\lim_{x\rightarrow 0}\frac{3\sin(4x)}{\sin(3x)}=\lim_{x\rightarrow 0}4\frac{\sin(4x)}{4x} \ \frac{3x}{\sin(3x)}[/tex]
Both of those limits are equal to the know limit for sin(x)/x
That would mean for any point on the graph (c,f(c)) -1<c<1zell_D said:o wow that was much ezier thanks a lot guys, sorry for all the bothering =/
and lasty, i am suppose to state whether this statement is true or false with this graph, obviously i can't draw the graph on here but would one of you tell me what does:
lim x-> c f(x) exists at every c in (-1, 1) mean?
A limit is a fundamental concept in calculus that represents the value that a function approaches as its input (or independent variable) approaches a certain value. In other words, it is the value that a function gets closer and closer to, but does not necessarily equal, as its input gets closer and closer to a specific value.
To solve a limit, you must first plug in the value that the independent variable is approaching into the given function. Then, you can use algebraic techniques, such as factoring or simplifying, to manipulate the function and find the limit. In some cases, you may need to use special limit theorems or techniques, such as L'Hopital's rule, to solve the limit.
A one-sided limit is when the independent variable approaches the given value from only one direction, either from the left or the right. A two-sided limit is when the independent variable approaches the given value from both directions, and the limit exists only if the one-sided limits from both directions are equal.
If the limit does not exist, it means that the function does not approach a single value as the independent variable gets closer and closer to the given value. This can happen for various reasons, such as the function having a jump or a discontinuity at that point, or the function oscillating infinitely around that point.
To solve this particular limit, you can use the fact that sin x/x approaches 1 as x approaches 0. By substituting x=4x/4x in the given function, you can rewrite it as (3/4)(sin 4x)/(sin 3x/4x). As x approaches 0, the first fraction approaches (3/4), and the second fraction approaches 1. Therefore, the limit is (3/4).