Civil Engineering (CE) Exam > Civil Engineering (CE) Questions > Let f (x) =. Then f(100)(54) is given bya)Und...
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Let f (x) = 
. Then f(100)(54) is given by
. Then f(100)(54) is given by- a)Undefined
- b)100
- c)10
- d)0
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Let f (x) =. Then f(100)(54) is given bya)Undefinedb)100c)10d)0Correct...
Concept:
Taylor’s series method:
The Taylor series can be used to calculate the value of an entire function at every point, if the value of the function, and all of its derivatives, are known at a single point.
Taylor's series expansion for f (x + h) is
f(x+h) = f(x) + hf′(x) + h2/2!f″(x) + h3/3! + f‴(x)+…∞
f(x) = f(a) + (x−α)f′(x) +
(x) +........∞
f(x+h) = f(x) + hf′(x) + h2/2!f″(x) + h3/3! + f‴(x)+…∞
f(x) = f(a) + (x−α)f′(x) +
(x) +........∞Calculation:
Given:
f(100)(54) = ?
Using Taylor series expansion for Sin x at a = 54
f(100)(54) = ?
Using Taylor series expansion for Sin x at a = 54
Now the function transforms into:
After Observing carefully the first term in the above infinite series, the (x - 54) term is always in the denominator, which will become zero when we put x = 54.
Every derivative will also have the same term till infinite.
So, every term will have zero in its denominator after putting x = 54.
⇒ f(100)(54) is Undefined.
Most Upvoted Answer
Let f (x) =. Then f(100)(54) is given bya)Undefinedb)100c)10d)0Correct...
Concept:
Taylor’s series method:
The Taylor series can be used to calculate the value of an entire function at every point, if the value of the function, and all of its derivatives, are known at a single point.
Taylor's series expansion for f (x + h) is
f(x+h) = f(x) + hf′(x) + h2/2!f″(x) + h3/3! + f‴(x)+…∞
f(x) = f(a) + (x−α)f′(x) +(x) +........∞
f(x+h) = f(x) + hf′(x) + h2/2!f″(x) + h3/3! + f‴(x)+…∞
f(x) = f(a) + (x−α)f′(x) +
(x) +........∞Calculation:
Given:
f(100)(54) = ?
Using Taylor series expansion for Sin x at a = 54
f(100)(54) = ?
Using Taylor series expansion for Sin x at a = 54
Now the function transforms into:
After Observing carefully the first term in the above infinite series, the (x - 54) term is always in the denominator, which will become zero when we put x = 54.
Every derivative will also have the same term till infinite.
So, every term will have zero in its denominator after putting x = 54.
⇒ f(100)(54) is Undefined.
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Let f (x) =. Then f(100)(54) is given bya)Undefinedb)100c)10d)0Correct answer is option 'A'. Can you explain this answer?
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Let f (x) =. Then f(100)(54) is given bya)Undefinedb)100c)10d)0Correct answer is option 'A'. Can you explain this answer? for Civil Engineering (CE) 2025 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about Let f (x) =. Then f(100)(54) is given bya)Undefinedb)100c)10d)0Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let f (x) =. Then f(100)(54) is given bya)Undefinedb)100c)10d)0Correct answer is option 'A'. Can you explain this answer?.
Let f (x) =. Then f(100)(54) is given bya)Undefinedb)100c)10d)0Correct answer is option 'A'. Can you explain this answer? for Civil Engineering (CE) 2025 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about Let f (x) =. Then f(100)(54) is given bya)Undefinedb)100c)10d)0Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let f (x) =. Then f(100)(54) is given bya)Undefinedb)100c)10d)0Correct answer is option 'A'. Can you explain this answer?.
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