sin(6x) + xf(x) = 0
xf(x) = - sin(6x)
f(x) = - (sin6x)/x
lim(x-->0) [6 + f(x)]/x²
= lim(x-->0) [6 - (sin6x)/x]/x²
= lim(x-->0) [6x - sin(6x)]/x³
= lim(x-->0) [6 - 6cos(6x)]/(3x²) <== 洛必达法则
= lim(x-->0) [- 6(- 6)sin(6x)]/(6x) <== 再洛必达法则
= lim(x-->0) 36 · sin(6x)/(6x)
= 36
已知,lim x→0 [sin6x+xf(x)]\/x^3=0 求:lim x→0 [6+f(x)]\/x^2=...
lim(x-->0) [sin(6x) + xf(x)]\/x³ = 0，要弄做不定式，分子和分母都要趋向0 sin(6x) + xf(x) = 0 xf(x) = - sin(6x)f(x) = - (sin6x)\/x lim(x-->0) [6 + f(x)]\/x²= lim(x-->0) [6 - (sin6x)\/x]\/x²= lim(x-->0) [6x - s...
已知lim x→0 [sin6x+xf(x)]\/x^3=0, 求 lim x→0 [6+f(x)]\/x^2...
lim x→0 [sinx-x]\/x^3，如果按照你的那种做法，显然结果是0。实际上答案是-1\/6.此处应用的是一个很重要的公式——泰勒公式（只展开有限项目，后边的高阶项可视为高阶无穷小）sinx=x-1\/6*x^3.回到你的这道题，lim [sin6x+xf(x)]\/x^3=0 也就是 lim[6x-1\/6*(6x)^3+xf(x)...
已知lim x→0 [sin6x+xf(x)]\/x^3=0, 求 lim x→0 [6+f(x)]\/x^2...
简单计算一下即可，答案如图所示
lim x→0 [sin6x+xf(x)]\/x^3=0,求 lim x→0 [6+f(x)]\/x^2
因为lim x→0 [sin6x\/(6x)]=1 所以,lim x→0 [sin6x+xf(x)]\/x^3 =lim x→0 [6x+xf(x)]\/x^3 =lim x→0 [6+f(x)]\/x^2 =0
lim(x趋近于0)[sin6x+xf(x)]\/x^3=0,则lim(x趋近于0)[6+f(x)]\/x^2=?
,lim(x趋近于0)[sin6x+xf(x)]\/x^3=0,则知道f(x) 是低天X^2的。所以（6+F(X)）是低于X^2的。从而 lim(x趋近于0)[6+f(x)]\/x^2=0.
x趋于0,lim x-o ( sin6x+xf(x))\/x3=0 ,lim x-o (6+f(x))\/x2=?
解析：实际上，所要求的极限就是原极限的变形！原式＝lim(x→0)[sin6x＋xf(x)]\/x³＝lim(x→0)［x(sin6x)\/x＋f(x)］\/x³＝lim(x→0)［x(6sin6x)\/6x＋f(x)］\/x³＝lim(x→0)[6＋f(x)]\/x²＝0 导数第二步就是所要求的。即 lim(x→0)[6＋f(...
...sin6x+xf(x))\/x^3=0,求limx趋近于0,(6+f(x))\/x^2的值
lim x→0,[sin6x + xf(x)]\/x³=0+α，其中lim x→0,α=0 即f(x)\/x² = -sin6x\/x³ + α 从而lim x→0,[6+f(x)]\/x²=lim x→0,( 6\/x² - sin6x\/x³ + α )=lim x→0,(6x-sin6x)\/x³，用洛必达法则 =lim x→0,[...
若极限lim(x-0)[sin6x+xf(x)]\/x^3=0,则lim(x-0)[6+f(x)]\/x^2=?
简单计算一下即可，答案如图所示
若lim [sin6x+xf(x)]\/x^3=0,则lim [6+f(x)]\/x^2是多少? (x是趋近0)
lim [sin6x+xf(x)]\/x^3=0,则lim [6+f(x)]\/x^2是36（x是趋近0）(x→0)lim[sin6x+xf(x)]\/x^3=0 属于0-0型，可以应用洛必答法则：(x→0)lim[6cos6x+f(x)+xf'(x)]\/(3x^2)=0 (x→0)lim[-36sin6x+f'(x)+f'(x)+xf''(x)]\/(6x)=0 (x→0)lim[-216cos...
求极限当x→0若lim[sin6x+x f(x)]\/x3=0,求lim[6+ f(x)]\/x2
代入得到 lim[sin6x+xf(x)]\/x^3=6x-(6x)^3\/3!+o(x^3)+f(0)x+f'(0)x^2+1\/2f''(0)x^3+o(x^3)\/x^3=0 x→0 整理得lim[6x+f(0)x+f'(0)x^2]\/x^3+1\/2f''(0)-36=0 从而f(0)=-6 f'(0)=0 1\/2f''(0)-36=0 f''(0)=72 lim[6+ f(x)]\/x^2=...
