Question
Evaluate the limit:Â
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ATQ,
We will use the Taylor series expansion for e2x around x = 0. The Taylor series expansion of e2x 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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