Question

Let y = tan x (a) Find the differential dy. dy = ?(b) Evaluate dy and ∆y if x= π/3 and dx = -0.2 (round ∆y to four decimal places)dy=?∆y=?

Answer 1

y = tan x

a)

dy = 1/cos^2 x = sec^2 x

$dy\text{ = }\frac{1}{\cos^2x}=\sec ^2x$

b)

y = f(x) ==> ∆y = f(x + ∆x) - f(x)

∆y = tan(π/3 - 0.2) - tan(π/3) = −0.00349

∆y = −0.0035