If (x^4)/((x-1)(x-2))=(16)/(x-2)-(1)/(x-...

If `(x^4)/((x-1)(x-2))=(16)/(x-2)-(1)/(x-1)+x^(2)+3 x+k` ,then `k=`

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To solve the equation \[ \frac{x^4}{(x-1)(x-2)} = \frac{16}{x-2} - \frac{1}{x-1} + x^2 + 3x + k, \] we need to find the value of \( k \). ### Step 1: Find a common denominator for the right-hand side The common denominator for the terms on the right-hand side is \( (x-1)(x-2) \). So, we can rewrite the right-hand side as: \[ \frac{16(x-1)}{(x-2)(x-1)} - \frac{1(x-2)}{(x-1)(x-2)} + (x^2 + 3x + k)(x-1)(x-2). \]

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If the third derivative of (x^(4))/((x-1)(x-2)) is (-12k)/((x-2)^(4))+(6)/((x-1)^(4)) , then the value of k is

If int(dx)/(x^(3)(x-1)^(1//2))=(sqrt(x-1)(3x+2))/(4x^(2)) + K tan^(-1)sqrt(x + 1) + C then the value of K is

`1//2`

`1//4`

`3//4`

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.

`5/3`

`1/3`

`2/3`

`8/3`