Question

高数第9题求解

手写最好

Answer 1

求cos29°=cos(29π/180)的近似值；
解：作函数 y=cosx；取xo=π/6; ∆x=-1°=-π/180 ; cosxo=cos(π/6)=cos30°=0.866；
y'=-sinθ； y'(xo)=-sin(π/6)=-1/2;
故 cos29°=cos30°+(-1/2)(-π/180)≈0.866+0.5×0.017=0.8745;
公式：f(xo+∆x)=f(xo)+f'(xo)•∆x

Answer 2

cos(29) = cos(30-1) ~ cosx + (cosx)' (-pi/180), where x = pi/6
结果 = cospi/6 + sin(pi/6) pi/180 = .874752