📢 Too many exams? Don’t know which one suits you best? Book Your Free Expert 👉 call Now!


    Question

    Evaluate the limit: 

    src="data:image/png;base64,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" alt="" />
    A 5 Correct Answer Incorrect Answer
    C 2 Correct Answer Incorrect Answer
    D 1 Correct Answer Incorrect Answer

    Solution

    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

    Practice Next
    ask-question