Question

I have to evaluate the limit of these problems and I can't figure them out!

1.) Lim
x-> 1
x^2+x-2/x^2-x

2.) (please note that the -2 is not under the square root)
Lim
x->0
sqroot 4+h -2/ h

Answer 1

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