[ASK] Limit of Trigonometry Function

In summary, the limit of a trigonometry function is the value that the function approaches as the input approaches a particular value. This can be found using algebraic manipulation or graphing techniques. The significance of the limit is that it helps us understand the behavior of the function at a specific point and determine if it is continuous. Common trigonometry functions that have limits include sine, cosine, tangent, cotangent, secant, and cosecant. However, the limit can also be undefined if the function has a vertical asymptote or if the approaching value causes the function to be undefined.
  • #1
Monoxdifly
MHB
284
0
\(\displaystyle \lim_{x\to0}\frac{sin2x+sin6x+sin10x-sin18x}{3sinx-sin3x=}\)
A. 0
B. 45
C. 54
D. 192
E. 212

Either substituting or using L'Hopital gives \(\displaystyle \frac00\). Is there any way to simplify it and make the result a real number?
 
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  • #2
We can repeat L'Hôpital until it's not $\frac 0 0$ any more.
 
  • #3
Ah, I see. It's in the third derivative and the answer is \(\displaystyle \frac{4,608}{24}\)= 192, right?
 
  • #4
Monoxdifly said:
Ah, I see. It's in the third derivative and the answer is \(\displaystyle \frac{4,608}{24}\)= 192, right?
Yep. (Nod)
 

FAQ: [ASK] Limit of Trigonometry Function

What is the limit of a trigonometry function?

The limit of a trigonometry function is the value that the function approaches as its input variable gets closer and closer to a specific value. It is an important concept in calculus and is often used to determine the behavior of a function at a certain point.

How do you find the limit of a trigonometry function?

To find the limit of a trigonometry function, you can use various techniques such as substitution, factoring, and trigonometric identities. You can also use the rules of limits, such as the sum, difference, and product rules, to simplify the function and evaluate the limit.

What is the difference between a one-sided and two-sided limit of a trigonometry function?

A one-sided limit only considers the behavior of the function from one side of the input value, while a two-sided limit considers the behavior from both sides. In other words, a one-sided limit only looks at the values approaching from the left or right of the input value, while a two-sided limit considers both.

What is the significance of the limit of a trigonometry function?

The limit of a trigonometry function helps us understand the behavior of the function at a specific point and can be used to determine if the function is continuous or discontinuous at that point. It also has applications in real-world problems, such as finding the maximum or minimum values of a function.

Can the limit of a trigonometry function be undefined?

Yes, the limit of a trigonometry function can be undefined if the function has a vertical asymptote or if the function oscillates between two values as the input variable approaches a certain value. In these cases, the limit does not exist because the function does not approach a specific value.

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