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Calculate the values of (a), (b), and (c) in the following limits: (a) lim_(x->pi/2) (ln(sin x)/(1- sin x)), (b) lim_(x->‚àû) (1 + 2/x)ˣ, (c) lim_(x->1/2) (x/(2-x)²)

Answer :

Final answer:

The values of (a), (b), and (c) in the given limits are 1, e², and -4 respectively.

Explanation:

To calculate the values of (a), (b), and (c) in the given limits:

(a) lim(x->pi/2) (ln(sin x)/(1- sin x)) = 1

(b) lim(x->∞) (1 + 2/x)x = e2

(c) lim(x->1/2) (x/(2-x)2) = -4

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