1、lim((4^n-3^(n+1)))除以((2^(2n+1))+3^n) 当n 趋向于无穷 求极限2、已知y=((x/2)乘以√((x^2+1))) - (1/2)乘以ln(x+√(x^2+1)),求y' 即对y求导3求y=3^(-x)的n阶导数4 lim (x/lnx-1/(x-1)) 当x趋向于1
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![1、lim((4^n-3^(n+1)))除以((2^(2n+1))+3^n) 当n 趋向于无穷 求极限2、已知y=((x/2)乘以√((x^2+1))) - (1/2)乘以ln(x+√(x^2+1)),求y' 即对y求导3求y=3^(-x)的n阶导数4 lim (x/lnx-1/(x-1)) 当x趋向于1](/uploads/image/z/8686891-19-1.jpg?t=1%E3%80%81lim%28%284%5En-3%5E%EF%BC%88n%2B1%29%29%29%E9%99%A4%E4%BB%A5%28%282%5E%282n%2B1%29%29%2B3%5En%29+%E5%BD%93n+%E8%B6%8B%E5%90%91%E4%BA%8E%E6%97%A0%E7%A9%B7+%E6%B1%82%E6%9E%81%E9%99%902%E3%80%81%E5%B7%B2%E7%9F%A5y%3D%28%28x%2F2%29%E4%B9%98%E4%BB%A5%E2%88%9A%EF%BC%88%28x%5E2%2B1%29%29%EF%BC%89+-+%281%2F2%29%E4%B9%98%E4%BB%A5ln%28x%2B%E2%88%9A%EF%BC%88x%5E2%2B1%29%29%2C%E6%B1%82y%27+%E5%8D%B3%E5%AF%B9y%E6%B1%82%E5%AF%BC3%E6%B1%82y%3D3%5E%28-x%29%E7%9A%84n%E9%98%B6%E5%AF%BC%E6%95%B04+lim+%28x%2Flnx-1%2F%28x-1%29%29+%E5%BD%93x%E8%B6%8B%E5%90%91%E4%BA%8E1)
1、lim((4^n-3^(n+1)))除以((2^(2n+1))+3^n) 当n 趋向于无穷 求极限2、已知y=((x/2)乘以√((x^2+1))) - (1/2)乘以ln(x+√(x^2+1)),求y' 即对y求导3求y=3^(-x)的n阶导数4 lim (x/lnx-1/(x-1)) 当x趋向于1
1、lim((4^n-3^(n+1)))除以((2^(2n+1))+3^n) 当n 趋向于无穷 求极限
2、已知y=((x/2)乘以√((x^2+1))) - (1/2)乘以ln(x+√(x^2+1)),求y' 即对y求导
3求y=3^(-x)的n阶导数
4 lim (x/lnx-1/(x-1)) 当x趋向于1
1、lim((4^n-3^(n+1)))除以((2^(2n+1))+3^n) 当n 趋向于无穷 求极限2、已知y=((x/2)乘以√((x^2+1))) - (1/2)乘以ln(x+√(x^2+1)),求y' 即对y求导3求y=3^(-x)的n阶导数4 lim (x/lnx-1/(x-1)) 当x趋向于1
看图
解(1):原式=lim(n->∞){[1-3(3/4)^n]/[2+(3/4)^n]} (分子分母同除4^n)
=(1-3*0)/(2+0) (∵lim(n->∞)[(3/4)^n]=0)
=1/2;
解(2):∵y=(x/2)√(x²+1)-(1/2)ln[x+√(x²+1)]
∴y'=(...
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解(1):原式=lim(n->∞){[1-3(3/4)^n]/[2+(3/4)^n]} (分子分母同除4^n)
=(1-3*0)/(2+0) (∵lim(n->∞)[(3/4)^n]=0)
=1/2;
解(2):∵y=(x/2)√(x²+1)-(1/2)ln[x+√(x²+1)]
∴y'=(1/2)√(x²+1)-x²/[2√(x²+1)]-1/[2√(x²+1)]
=(1/2)√(x²+1)-(1/2)√(x²+1)
=0;
解(3):∵y=3^(-x)
∴y'=3^(-x)*(-ln3)
y''=3^(-x)*(-ln3)²
y'''=3^(-x)*(-ln3)³
.......
y的k阶导数=3^(-x)*(-ln3)^k
.......
故y=3^(-x)的n阶导数=3^(-x)*(-ln3)^n;
解(4):原式=lim(x->1){[x(x-1)-lnx]/[(x-1)lnx]} (分式通分)
=lim(x->1)[(2x²-x-1)/(x+xlnx)] (0/0型,应用罗比达法则)
=lim(x->1)[(4x-1)/(2+lnx)] (0/0型,应用罗比达法则)
=(4-1)/(2+0)
=3/2.
收起
1) 分子分母同除以4^n 再求 =1/2
2) 第一个按乘积的求导法则,第二项按复合函数,先ln,在()
3)=(-1)^n * 3^(-x)*(ln3)^n
4) 通分,用两次罗比他法则 =3/2