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The series expansion of sinx/x near origin is
- a)
- b)
- c)
- d)
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
The series expansion ofsinx/x near origin isa)b)c)d)Correct answer is ...
Concept:
Taylor series:
The Taylor series of a real or complex-valued function f (x) that is infinitely differentiable at a real or complex number ‘a’ is the power series.
Expression of Taylor series is:
Calculation:
Calculation:
Given:
We have to find the series expansion of sinx/x near origin, or a = 0.
Let f(x) = sin x
f(0) = sin (0) = 0,
f'(0) = cos (0) = 1,
f''(0) = -sin(0) = 0,
f'''(0) = -1 .... so on
Putting all the values in Taylor series expansion, we get:
Series expansion of sin x will be:
sinx = x − x3/3!+…
Therefore the series expansion of sin x/x near origin will be:
sinx = x − x3/3!+…
Therefore the series expansion of sin x/x near origin will be:
Most Upvoted Answer
The series expansion ofsinx/x near origin isa)b)c)d)Correct answer is ...
Concept:
Taylor series:
The Taylor series of a real or complex-valued function f (x) that is infinitely differentiable at a real or complex number ‘a’ is the power series.
Expression of Taylor series is:
Calculation:
Calculation:
Given:
We have to find the series expansion of sinx/x near origin, or a = 0.
Let f(x) = sin x
f(0) = sin (0) = 0,
f'(0) = cos (0) = 1,
f''(0) = -sin(0) = 0,
f'''(0) = -1 .... so on
Putting all the values in Taylor series expansion, we get:
Series expansion of sin x will be:
sinx = x − x3/3!+…
Therefore the series expansion of sin x/x near origin will be:
sinx = x − x3/3!+…
Therefore the series expansion of sin x/x near origin will be:
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Question Description
The series expansion ofsinx/x near origin isa)b)c)d)Correct answer is option 'C'. Can you explain this answer? for Civil Engineering (CE) 2026 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about The series expansion ofsinx/x near origin isa)b)c)d)Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The series expansion ofsinx/x near origin isa)b)c)d)Correct answer is option 'C'. Can you explain this answer?.
The series expansion ofsinx/x near origin isa)b)c)d)Correct answer is option 'C'. Can you explain this answer? for Civil Engineering (CE) 2026 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about The series expansion ofsinx/x near origin isa)b)c)d)Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The series expansion ofsinx/x near origin isa)b)c)d)Correct answer is option 'C'. Can you explain this answer?.
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