InterviewSolution
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InterviewSolution
| 1. |
Evaluate, `lim_(x to 1) (x^(4)-1)/(x-1)=lim_(x to k) (x^(3)-k^(3))/(x^(2)-k^(2))` , then find the value of k. |
| Answer» Given, `=underset(xto0)"lim"(x^(3)-k^(3))/(x^(2)-k^(2))`<br> `rArr 4(1)^(4-1)=underset(xtok)"lim"((x^(3)-k^(3))/(x-k))/((x^(2)-k^(2))/(x-k))` `[therefore underset(xtoa)"lim"(x^(n)-a^(n))/(x-a)=na^(n-1)]`<br> `rArr 4=(underset(xtok)"lim"(x^(3)-k^(3))/(x-k))/(underset(xtok)"lim"(x^(2)-k^(2))/(x-k))` `therefore underset(xtoa)"lim"(f(x))/(g(x))`<br> `rArr 4=(3k^(2))/(2k) rArr 4=3/2k`<br> `therefore k=(4 xx2)/(3)=8/3` | |