1] limits- lim ( e^tan h - 1)/h h->0 2] lim (e^(x+h)² - e^x²)/h h->0

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by Arunav5

2015-03-02T16:37:16+05:30

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We use the definition of e^x to solve this problem.

we use the following limits.

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the expression on the RHS simplifies as all the terms except tend to zero, as they contain h.

sir is there any other easier meathod its a 1 mark question.
take limit of h ->0 for derivative of numerator divided by derivative of denominator.
1) lim h->0 e^tan h * sec^2 h / 1 => e^0 * sec^2 0 = 1
Another way: given limit is the definition of e^tanh at h = 0. So evaluate its derivative and substitute h = 0.
2) same as above two methods.. given problem is same as the definition of the derivative of e^{x^2}. wrt x. so find it directly.