Question

(1) How can values of the function

$f(x) = \frac{\sqrt{1+x} - 1}{x}$

be computed accurately when x is sufficiently close to 0?

(2) How can values of the function

$g(x) = \frac{sin^{2}x}{1-cosx}$

be computed accurately when x is sufficiently close to 0?

Answer 1

use the method of limits to solve the problem I lim (With I) It is form of o 7 denominator altn multiplying numerator & by Vint nto Ato It - limon Gregorian +75) - limo (viento) e formended = 1 [F (M) = 4 when a is sufficiently close to

un g form no X70 - X - lim ((2 sin ..c092)* ) Izsinxel a sin Formula used: sind=2 sinh cos/ In lobo 2 sin2o% no = lim 4 sin cos2 ) no ( 2 sinh ) Elim (.2 603*192) he form endest put nao g(n)=2 when a is sufficiently close to o
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