Step-by-step explanation:
15. [tex]f(2+h) = (2 + h)^2 - (2 +h) + 1[/tex]
[tex]\:\:\:\:\:\:\:= 3 + 3h + h^2[/tex]
[tex]f(2) = (2)^2 - (2) + 1 = 3[/tex]
Therefore,
[tex]\dfrac{f(2+h) - f(2)}{h} = \dfrac{3h + h^2}{h}[/tex]
[tex]\:\:\:\:\:\:\:= 3 + h[/tex]
16. [tex]f(x + h) = 5(x + h) - (x + h)^2[/tex]
[tex]\:\:\:\:\:\:\:= 5x + 5h - x^2 - 2hx - h^2[/tex]
Therefore,
[tex]\dfrac{f(x+h) - f(x)}{h} = \dfrac{5h - 2hx - h^2}{h}[/tex]
[tex]\:\:\:\:\:\:\:= 5 - 2x - h[/tex]
