Compute Difference Quotient

[nycmath]

Precalculus
David Cohen
Edition 3
Chapter 3, Srction 3.1

Compute the difference quotient for the function.

See attachment.

[Eigenvalue]

43. [tex]\frac{8x+8h-3-8x+3}{h}[/tex]
=[tex]\frac{8x}{8}[/tex]
=h

44. [tex]\frac{-2x-2h+9+2x-9}{h}[/tex]
=[tex]\frac{-2h}{h}[/tex]

45a. [tex]\frac{(x+h)²-x²}{h}[/tex]
=[tex]\frac{2hx+h²}{h}[/tex]
=2x+h

45b. [tex]\frac{2(x+h)²-2x²}{h}[/tex]
=[tex]\frac{4xh+2h²}{h}[/tex]
=4x+2h

45c. [tex]\frac{2(x+h)³-2x³}{h}[/tex]
=[tex]\frac{6x²h+6xh²+2h³}{h}[/tex]
=6x²+6xh+2h²

45d. [tex]\frac{2(x+h)⁴-2x⁴}{h}[/tex]
=[tex]\frac{8x³h+12x²h²+8xh³+2h⁴}{h}[/tex]
=8x³+12x²h+8xh²+2h³

46a. [tex]\frac{-3(x+h)²-3x²}{h}[/tex]
=[tex]\frac{-6xh+h²}{h}[/tex]
=-6x+h