How did this transition occur?

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In summary, the conversation discusses the equation lim as x-> 0 (2-cos3x-cos4x)/(x) and questions how the numerator became (1-cos3x)(1-cos4x)/(x). It is suggested that the correct form should be (1-cos3x) + (1-cos4x).
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kLPantera
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lim as x-> 0 (2-cos3x-cos4x)/(x).

I'm not sure how the numerator became (1-cos3x)(1-cos4x)/(x)

What am I missing? Could someone please point it out? Is it a trignometric factoring formula I'm not thinking of?
 
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  • #2
kLPantera said:
lim as x-> 0 (2-cos3x-cos4x)/(x).

I'm not sure how the numerator became (1-cos3x)(1-cos4x)/(x)

What am I missing? Could someone please point it out? Is it a trignometric factoring formula I'm not thinking of?
It's difficult to answer this without you providing more context, but here's a try.

(2-cos(3x)-cos(4x)) ≠ (1-cos(3x))(1-cos(4x)).

However, (2-cos(3x)-cos(4x)) = (1-cos(3x)) + (1-cos(4x)) .
 
  • #3
So how did the numerator become: (2-cos(3x)-cos(4x)) = (1-cos(3x)) + (1-cos(4x))?
 

FAQ: How did this transition occur?

How did this transition occur?

The transition occurred through a series of gradual changes and adaptations over a long period of time. It is believed that natural selection played a major role in driving this transition.

What evidence supports this transition?

There is a vast amount of evidence from various fields of science, including genetics, paleontology, and comparative anatomy, that supports the idea of gradual evolution and the transition between species.

Was there a specific cause for this transition?

While there is no single cause for this transition, it is believed that changes in the environment and competition for resources may have played a role in driving species to adapt and evolve over time.

How long did this transition take?

The length of time for this transition varies depending on the species and the specific changes that occurred. Some transitions may have taken thousands of years, while others may have taken millions of years.

Are there any ongoing transitions occurring currently?

Yes, evolution is an ongoing process and there are many examples of species undergoing gradual changes and transitions in response to environmental pressures and other factors.

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