高数极限例题及详解 大一高数极限经典例题
\u9ad8\u6570\u6781\u9650\u4f8b\u9898\u53ca\u8be6\u89e3 (\u6c42\u5bfc)a = [f''(0)]/2\uff1bb = f'(0)\uff1bc = f(0)
\uff0d\uff0d\uff0d\uff0d\uff0d\uff0d\uff0d\uff0d\uff0d\uff0d\uff0d\uff0d\uff0d\uff0d\uff0d\uff0d
\u89e3\u6790\uff1a
\u4ee4 g(x) = ax^2 + bx + c;
\u5219 g'(x) = 2ax + b
g''(x) = 2a
\u4e8c\u9636\u53ef\u5bfc\uff0c\u5373\u4e8c\u9636\u5bfc\u6570\u5b58\u5728\uff0c\u56e0\u6b64\uff1a
f''(0) = lim(x\u21920) [g''(x)] = 2a
a = [f''(0)]/2
\u56e0\u4e3a\u4e8c\u9636\u5bfc\u6570\u5b58\u5728\uff0c\u6240\u4ee5\u4e00\u9636\u5bfc\u6570 [\u5b58\u5728] \u4e14 [\u8fde\u7eed]\uff0c\u56e0\u6b64\uff1a
f'(0) = lim(x\u21920) [g'(x)] = b
\u56e0\u4e3a\u4e00\u9636\u5bfc\u6570\u5b58\u5728\uff0c\u6240\u4ee5\u539f\u51fd\u6570 [\u8fde\u7eed]\uff0c\u56e0\u6b64\uff1a
f(0) = lim(x\u21920) [g(x)] = c
\u6240\u4ee5 g(x) = [f''(0)]*(x^2)/2 + f'(0) + f(0)
只需要配成(x-2)^2+(x-2)的形式就可以了
首先是化成（x-2）^2+7(x-2)+(k+10)，这是分母上面
然后分开带进去，有lim[(x-2)+7+(k+10)/(x-2)]=7，只要让k+10=0就可以了
因为分母的极限是0，那么分子在x趋向2时的极限也应该是0，否则极限是无穷，不存在
所以k=-（2*2+3*2）=-10
供参考~
x^2-3x+k 因式分解成 (x-2)*(x+5),所以k=-10
x^2+3x+k=7x-14
令x=2
解得k=-10
负10，这个明显分母为0那么分子也必须为0不然就是无解，有x=2时分子为0可得k为-10
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