Answer each question with a minimum of 70 words per question:Discuss the Weierstrass Approximation...

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Answer each question with a minimum of 70 words per question:Discuss the Weierstrass Approximation Theorem. When would you use this theorem? Are there other options for solving these types of problems besides the Weierstrass Approximation Theorem?Discuss the pros and cons for Lagrange interpolations. Be sure to provide specific examples of both pros and cons, and include citations and references for all sources used.
	
Document Preview: Answer each question with a minimum of 70 words per question:Discuss the Weierstrass Approximation Theorem. When would you use this theorem? Are there other options for solving these types of problems besides the Weierstrass Approximation Theorem?Discuss the pros and cons for Lagrange interpolations. Be sure to provide specific examples of both pros and cons, and include citations and references for all sources used.

Robert · Accepted Answer

Question: Discuss the Weierstrass Approximation Theorem. When would you use this 
theorem? Are there other options for solving these types of problems besides the 
Weierstrass Approximation Theorem? 
Answer: “If is a continuous real-valued function on  and if any is given, then there 
exists a polynomial  on such that
for all . In words, any continuous function on a closed and bounded interval can be 
uniformly approximated on that interval by polynomials to any degree of accuracy.” (Weisstein, 
n.d) 
This theorem can be used when the function is unimodal and continuous over the closed and 
bounded interval.

Answer each question with a minimum of 70 words per question:Discuss the Weierstrass Approximation Theorem. When would you use this theorem? Are there other options for solving these types of problems...

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