Evaluating Limit: Sin(x + Sin x) at x=π

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SUMMARY

The limit of the function Sin(x + Sin x) as x approaches π is evaluated using continuity principles. The function is continuous within its domain, as it is a combination of algebraic and trigonometric functions. By substituting π into the function, the result approaches 0.05575, indicating that the limit exists and is finite. The discussion emphasizes the importance of understanding the continuity of functions when evaluating limits.

PREREQUISITES
  • Understanding of trigonometric functions, specifically Sin(x)
  • Knowledge of limits in calculus
  • Familiarity with the concept of continuity in mathematical functions
  • Basic algebraic manipulation skills
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  • Study the properties of continuous functions in calculus
  • Learn about evaluating limits using substitution techniques
  • Explore the relationship between trigonometric functions and their limits
  • Investigate the implications of continuity on the behavior of functions
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powp
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Hello

can someone help me with this question??

Use continuity to evaluate the limit:

lim x->PI Sin(x + Sin x)

Please!

thanks
 
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a) Is that function continuous?
b) What is definition of continuity?
Combine the two and the answer is trivial.
 
I believe that this function is continus within its domain because it is a algebaric and trig function.

But where do I go from here. If I plug Pi into the function I get 0.00
 
sorry I get 0.05575
 
powp said:
sorry I get 0.05575

What is \sin \pi? I think you'll find your calc is in degrees not radians.
 
Let f(x)=x+sin(x), and let g(x)=sin(x). What is g(f(x))?
 

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