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Linearization And Differentials:

If ƒ(x) is a differentiable real function at x=a, then the approximating function   t(x) =ƒ(a) + ƒ′(a) (x – a)  is called the linearization of f at a.

 

Linearization And Differentials Sample Questions:

Question 1: Estimate 11,907 + 3,789

 

(a) 4

(b) 3

(c) 2

(d) 1


Answer: (c)

Explanation:

 

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Question 2:



Answer: (b)

Explanation:

 

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Question 3: 

 


Answer: (c)

Explanation:

 

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Question 4: 

 


Answer: (a)

Explanation:

 

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Question 5: 


Answer: (a)

Explanation:

 

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Question 6: 

 


Answer: (c)

Explanation:

 

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Question 7: 

 


Answer: (b)

Explanation:

 

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Question 8: Differentials are often constrained to be______?

 

(a) Very small quantities

(b) Very large quantities

(c) Constant

(d) None


Answer: (a)

Explanation: Differentials are often constrained to be very small quantities.

 

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Question 9: A linear approximation normally loses accuracy away from its ____?

 

(a) Extreme points

(b) Center

(c) Both

(d) None


Answer: (b)

Explanation: If ƒ(x) is a differentiable real function at x=a, then the approximating function t (x) =ƒ(a) + ƒ′(a) (x – a) is called the linearization of f at a.

 

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Question 10: 


Answer: (c)

Explanation:

 

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