Both 10 and 11 Thanks Determine the limits below by direct s

Determine the limits below by direct substitution, dividing or numerators: lim_x rightarrow 2 x - 2/x^3 - 2x^2 + 2x - 4 =

Solution

10)

x-2)x³-2x²+2x-4(x²+2
......x³-2x²
...............0+2x-4
..................+2x-4
.........................0

lim_x->2(x-2)/(x³-2x²+2x-4)

=lim_x->2(x-2)/((x-2)(x²+2))

=lim_x->2 1/(x²+2)

=1/(2²+2)

=1/(4+2)

=1/6

11)lim_x->0[(x+9) -3]/x

multiply and divide by (x+9) +3

lim_x->0[((x+9) -3)((x+9) +3)]/[x((x+9) +3)]

lim_x->0[((x+9)² -3²)]/[x((x+9) +3)]

lim_x->0[((x+9) -9)]/[x((x+9) +3)]

lim_x->0[x]/[x((x+9) +3)]

lim_x->0 1/((x+9) +3)

=1/((0+9) +3)

=1/(3+3)

=1/6