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jog511
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Homework Statement
lim x->0 sin4x/2x
Homework Equations
lim x->0 sinx/x =1
The Attempt at a Solution
can I write lim x->0 sin4x/2x as sinx/x * 4/2 = 1*2 or am I missing a step ?
]No, one cannot do that. There is no rule that says one can pull out a factor from a trig function like this. You have to rewrite you expression in the formjog511 said:Homework Statement
lim x->0 sin4x/2x
Homework Equations
lim x->0 sinx/x =1
The Attempt at a Solution
can I write lim x->0 sin4x/2x as sinx/x * 4/2 = 1*2 or am I missing a step ?
I have no idea what you mean by that. But surely you know that sin(2x) is NOT equal to 2sin(x)?jog511 said:like 4/4
jog511 said:like 4/4
nrqed said:Set aside the limit for now. Try writing the expression in the form [itex] C \, \sin(y)/y [/itex]. What is y(x)? What is C?
jog511 said:sin4x/2x * 4/4 = 4*sin4x/4*2x
jog511 said:C = 4,
y(x) = 4x
jog511 said:I believe I get sin4x/4x
nrqed said:Hold on. If y =4x and C = 4 then
[itex] C \sin(y)/y = 4 \frac{ \sin(4x) }{4x} [/itex]
right? This is not the initial expression.
jog511 said:I don't understand this concept. Even Calculus by Larson does not explain it well.
jog511 said:c in the original equation was 1
Correct.jog511 said:It has to be 2
jog511 said:thanks for your patience
A trig function limit is a mathematical concept that involves finding the value that a trigonometric function approaches as its input variable approaches a certain value, usually denoted as x->a. In the case of lim x->0 sin4x/2x, we are looking for the value that the function sin4x/2x approaches as x gets closer and closer to 0.
To solve this limit, we can use the trigonometric identity lim x->0 sinx/x = 1. By substituting 4x for x in this identity, we get lim x->0 sin4x/4x = 1. Then, we can divide both the numerator and denominator of our original limit by 4 to get sin4x/2x = (1/4)sin4x/(1/2)2x. Using the limit identity again, we get (1/4)(1/2) = 1/8 as the final answer.
The input variable approaching 0 in this limit represents the behavior of the trigonometric function as it approaches 0, which is known as the limit point. This can help us understand the overall behavior of the function and determine its value at the limit point.
Yes, we can solve limits for other trigonometric functions using similar techniques and trigonometric identities. However, the specific approach may vary depending on the specific function and limit being evaluated.
Trig function limits have many applications in fields such as physics, engineering, and finance. They can help us analyze the behavior of various systems and predict their outcomes. For example, in physics, trig function limits can be used to calculate the velocity and acceleration of objects in motion, while in finance, they can be used to analyze the growth rate of investments.