GATE EE 2017 Set 1 — Question 2
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Engineering Mathematics → Complex Variables → Analytic Functions
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Question
For a complex number , is
Correct answer
(D) 2i
Solution
To find the limit , we first substitute into the expression to check for an indeterminate form.Numerator:
Denominator: Since the limit is in the indeterminate form , we apply L'Hôpital's rule by differentiating the numerator and the denominator with respect to :Now, substitute into the simplified expression:Thus, the limit is , which corresponds to option (D).
Denominator: Since the limit is in the indeterminate form , we apply L'Hôpital's rule by differentiating the numerator and the denominator with respect to :Now, substitute into the simplified expression:Thus, the limit is , which corresponds to option (D).
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