maths
posted by khela .
find the limit of
lim sin(x1)/(x^2 + x  2)
x>1

i interpreted this in two ways:
first,
lim [sin(x1)]/(x^2 + x  2) as x>1
*since, there is no common factor between numerator and denominator, it's in simplest form,, also you substitute 1 to both [sin(x1)] and (x^2 + x  2):
sin(x1) = sin (11) = 0
(x^2 + x  2) = i^2 + 1 2 = 0
lim 0/0 becomes indeterminate
*recall that when you have 0/0, you use L'hopital's Rule to get limit:
L'hopital's Rule: you get the derivative of both numerator and denominator,, then evaluate it at x,, thus:
derivative of sin(x1) = cos(x1)
derivative of (x^2 + x  2) = (2x + 1)
therefore,
[cos(x1)]/(2x + 1) evaluated at x=1
[cos(11)]/(2(1) + 1)
(cos(0))/(2+1)
you then solve it.