1.求隐函数x+y^2-e^(xy)=siny的倒数dy/dx2.计算√4.2的近似值（根号下4.2的近似值）2.计算√4.2的近似值（根号下4.2的近似值）3.求极限：limsin3x/ln(1+x)x→0

Question

1.求隐函数 x+y^2-e^(xy)=siny的倒数dy/dx 2.计算√4.2的近似值（根号下4.2的近似值）
2.计算√4.2的近似值（根号下4.2的近似值）
3.求极限：lim sin3x/ ln(1+x)
x→0

Answer 1

1
x+y^2-e^(xy)=1/siny
1+2yy'-(y+xy')e^(xy)=-y'cosy/(siny)^2
dy/dx=y'=[ye^(xy)-1]/[2y-xe^(xy)+cosy/(siny)^2]
2
y=√x,y'=1/2√x
[√(4.02)-√4]/(4.02-4)≈1/(2√4)
√4.02≈(1/4)*0.02+2=2.005
3
lim(x->0) sin3x/ln(1+x) x->0,sin3x->0,ln(1+x)->0
=lim(x->0)(sin3x)'/(ln(1+x))'
=lim(x->0)3cos3x/[1/(1+x)]
=3