Posted by please help! on Monday, June 18, 2012 at 12:01pm.
Whenever transcribing fractions, do not forget to insert parentheses around numerator AND denominator. The posted expressions do not evaluate into what you wanted to do.
1.
Factor numerator and denominator.
Reduce expression by cancelling common factors.
Evaluate remaining expression.
(x²+x-2)/(x²-x)
=(x+2)(x-1)/(x(x-1))
=(x+2)/(x)
evaluate limit for x → 1.
2.
Multiply top and bottom by conjugate, cancel out common factor and evaluate limit.
(√(4+h)-2)/(h)
=(√(4+h)-2)(√(4+h)+2)/((h)(√(4+h)+2))
=(4+h-2²)/(h(√(4+h)+2))
=h/(h(√(4+h)+2))
=1/(√(4+h)+2)
evaluate expression as x→0
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