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Question

Evaluate the limit:

A 5 Correct Incorrect

C 2 Correct Incorrect

D 1 Correct Incorrect

Detailed Solution

ATQ,

We will use the Taylor series expansion for e^2x around x = 0. The Taylor series expansion of e^2x around x = 0 is: This simplifies to: Now, substitute this into the given expression: Simplifying: Now, the limit becomes:

We can divide each term by x²:

As x→0, the terms involving x vanish, and we are left with = 2 Thus, the answer is = 2

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