Calculus Question

Question

Let y=tan(2x+4)

Find the differential dy when x=1 and dx=0.3

Find the differential dy when x=1 and dx=0.6

Answer 1

f'(x) = sec²(2x + 4)·2;

So, dy = f'(x)dx = 2sec²6 ·0.3 = 0.651.

dy = 2sec²6·0.6 = 1.302

·

Answer 2

dy/dx = 2sec²(2x+4)

dy = 2sec²(2x+4)dx

When x = 1 and dx = 0.3

dy = 2sec²(6)(0.3) = 0.6sec²(6) = 0.6(1.08)≈0.65

When x = 1 and dx =0.6

dy = 1.2(1.08) ≈ 1.296