Penjelasan dengan langkah-langkah:

1. lim x mendekati tak hingga

√(x²+5x+8)-√(x²+2x-1)

= lim x mendekati tak hingga

√(x²+5x+8)/x²-√(x²+2x-1)/x²

=lim x mendekati tak hingga

√(1+5/x+8/x²)-√(1+2/x-1/x²)

=√1 + 5/0 + 8/0² - √1 + 2/0 - 1/0²

= √1 - √1

= 0

2. lim x mendekati tak hingga

(4x-1)³/2x³-1

= (0 - 1)³/2(0)³-1

= -1³/-1

= -1/-1

= 1

3. lim x mendekati 3

(x² - 5x + 6)/(x - 3)

= lim x mendekati 3

((x - 3)(x - 2))/(x - 3)

= lim x mendekati 3

x - 2

= 3 - 2

= 1

4. lim x mendekati 0

(2x² - 5x)/3x

= lim x mendekati 0

2x/3 - 5/3

= 2(0)/3 - 5/3

= -5/3

5. lim x mendekati 3

(x² + 3x + 2)/(x² + x -2)

= (3² + 3(3) + 2)/(3² + 3 - 2)

= (9 + 9 + 2)/(9 + 3 - 2)

= 20/10

= 2

6. lim x mendekati tak hingga

(5x⁴ + 3x² - 2)/(2x⁵ + 2x + 1)

= (5(0)⁴ + 3(0)² - 2)/ (2(0)⁵ + 2(0) + 1)

= -2/1

= -2