Question

If y = f(x) = x2 + x, x = 10, ∆x = 0.1, find ∆y, dy.

Answer 1

Given y = x2 + x, x = 10 and ∆x = 0.1

∆y = f(x + ∆x) – f(x)

= (x + ∆x)2 + (x + ∆x) – (x2 + x)

= x2 + 2x ∆x + (∆x)2 + x + ∆x – x2 – x

= 2x ∆X + (∆x)2 + ∆x

= 2(10) (0.1) + (0.1)2 + 0.1

= 2 + 0.01 + 0.1

= 2.11

dy = f1 (x) ∆x

= (2x + 1) ∆x

= {2.(10) + 1} (0.1)

= (21) (0.1)

= 2.10.