Question

find the one sided limit of
a) x/(2x-1) x->1/2^+
b) (x^2-2x+1)/(x+1) x->-1^+

Answer 1

a) x/(2x - 1) = [1/2(2x - 1) + 1/2]/(2x - 1)

= 1/2 + 1/2(2x-1)

as x approaches 1/2 from above, the denominator of the second term approaches 0 from above, so the entire term will approach infinity

Answer 2

b) (x^2 - 2x + 1)/(x + 1) = (x - 1)^2/(x + 1) = (x + 1 - 2)^2/(x + 1)

= [(x + 1)^2 - 4(x + 1) + 4]/(x + 1)

= x + 1 - 4 + 4/(x + 1)

= x - 3 + 4/(x+1)

as x approaches -1 from above, the third term approaches positive infinity, so the entire expression approaches positive infinity

Answer 3

ANSWER FOR B IS -INFINTY

Answer 4

No, jamesm is right. notice how you approach -1 from above, so a sequence could be -0.9, -0.99, -0.999, ... For each of those number the denominator (x+1) will be positive, so the term goes to plus infinity.