limx→0 4x³-2x²+x3x²+2x

To evaluate this limit, we can use the fact that the limit of a quotient is the quotient of the limits, provided the denominator does not approach zero.

limx→0 (4x³-2x²+x)/(3x²+2x)

= limx→0 4x³/3x² + limx→0 (-2x²)/3x² + limx→0 x/3x² + limx→0 0/2x (dividing numerator and denominator by x)

= limx→0 (4/3)x + limx→0 (-2/3) + limx→0 (1/3x) + 0

= 0 + (-2/3) + ∞ + 0 (since the limit of 1/x as x approaches 0 is infinity)

= -2/3 + ∞

= ∞

Therefore, the limit is infinity.