MAT136H1 Chapter Notes - Chapter 6c: Ampicillin, Quadratic Function

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25 Jul 2018

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MATH136H1 –Class 6C – Series of Numbers

Approximating Curves – Theme of MATH135

A linear approximation for a curve  near  is the inear function  that most closely

approximates  for values of  near . For example, a tangent line

A quadratic approximation for a curve  near  is the quadratic function  that

most closely approximates  for the values of  near .

A cubic approximation for a curve  near  is the cubuc function  that most closely

approximates  for values of  near .

Question: Properties of linear approximation

Which of the following properties did the linear approximation  of function  near 

 have?

A. 

B. 

C. 

D. 

E. 

F. 

 



Options A and C are correct since both agree with above definition for linear approximation

Question: Properties of quadratic approximations

Which of the following properties did the quadratic approximation  of a function 

near  have?

A. 

B. 

C. 

D. 

E. 

F. 

 



Options A, C and D are correct since all three agree with the above definition of quadratic

approximation.

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A linear approximation for a curve (cid:1858)(cid:4666)(cid:4667) near = is the inear function (cid:4666)(cid:4667) that most closely approximates (cid:1858) for values of near . A quadratic approximation for a curve (cid:1858)(cid:4666)(cid:4667) near = is the quadratic function (cid:4666)(cid:4667) that most closely approximates (cid:1858) for the values of near . A cubic approximation for a curve (cid:1858)(cid:4666)(cid:4667) near = is the cubuc function (cid:4666)(cid:4667) that most closely approximates (cid:1858) for values of near . Which of the following properties did the linear approximation (cid:4666)(cid:4667) of function (cid:1858)(cid:4666)(cid:4667) near = (cid:882) have: (cid:4666)(cid:882)(cid:4667)=(cid:1858)(cid:4666)(cid:882)(cid:4667, (cid:4666)(cid:883)(cid:4667)=(cid:1858)(cid:4666)(cid:883)(cid:4667, (cid:4666)(cid:882)(cid:4667)=(cid:1858) (cid:4666)(cid:882)(cid:4667, (cid:4666)(cid:882)(cid:4667)=(cid:1858) (cid:4666)(cid:882)(cid:4667, (cid:4666)(cid:882)(cid:4667)=(cid:1858) (cid:4666)(cid:882)(cid:4667) lim (cid:4666)(cid:4667)= lim(cid:4666) (cid:4667)(cid:1858)(cid:4666)(cid:4667) Options a and c are correct since both agree with above definition for linear approximation. Which of the following properties did the quadratic approximation (cid:4666)(cid:4667) of a function (cid:1858)(cid:4666)(cid:4667) near =(cid:882) have: (cid:4666)(cid:882)(cid:4667)=(cid:1858)(cid:4666)(cid:882)(cid:4667, (cid:4666)(cid:883)(cid:4667)=(cid:1858)(cid:4666)(cid:883)(cid:4667, (cid:4666)(cid:882)(cid:4667)=(cid:1858) (cid:4666)(cid:882)(cid:4667, (cid:4666)(cid:882)(cid:4667)=(cid:1858) (cid:4666)(cid:882)(cid:4667, (cid:4666)(cid:882)(cid:4667)=(cid:1858) (cid:4666)(cid:882)(cid:4667) lim (cid:4666)(cid:4667)= lim(cid:4666) (cid:4667)(cid:1858)(cid:4666)(cid:4667)