GATE EC 2015 Set 3 — Question 5
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Engineering Mathematics → Calculus → Functions of Single Variable
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Question
If , which of the following must be true?i.
ii.
iii.
iv.
ii.
iii.
iv.
Correct answer
(A) (i) and (ii)
Solution
Given the condition :
1.Statement (i): . The natural logarithm function is strictly increasing for . Since , it follows that . This is true.
2.Statement (ii): . The exponential function is strictly increasing for all real . Since , it follows that . This is true.
3.Statement (iii): . This is not always true. For example, if and , then and . Here , so . This is not necessarily true.
4.Statement (iv): . The cosine function is not strictly increasing. For in the interval , is strictly decreasing. If , then . This is not necessarily true.
Thus, only statements (i) and (ii) must be true.Continue learning with Success Tracker
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