GATE ME 2016 Set 2 — Question 10
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Engineering Mathematics → Single Variable Calculus → Functions of Single Variable
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Question
Which of the following curves represents the function for ?
Here, represents the abscissa and represents the ordinate.
Here, represents the abscissa and represents the ordinate.
Correct answer
(C) [figure]
Solution
The given function is .
1.Since is always positive, .
2.Therefore, .
3.Since , the function simplifies to .
4.The graph of is always non-negative (). It consists of a series of positive 'humps' with zeros at and peaks of at .
5.Comparing this with the given options:
- (A) shows , which takes negative values.
- (B) shows , which also takes negative values.
- (C) correctly shows with zeros at .
- (D) shows a function with zeros at , which corresponds to .
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