What is the limit as x approaches 1 of ((x^{7a}-7ax+7a-1))/((x-1)^2) ?

The limit as x approaches 1 of ((x^{7a}-7ax+7a-1))/((x-1)^2) is (7a(7a-1))/2

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limit as x approaches 1 of ((x^{7a}-7ax+7a-1))/((x-1)^2)

x \to 1 lim (\frac{( x ^{7 a} - 7 a x + 7 a - 1 )}{( x - 1 ) ^{2}})

\frac{7 a ( 7 a - 1 )}{2}

Solution steps

x \to 1 lim (\frac{x ^{7 a} - 7 a x + 7 a - 1}{( x - 1 ) ^{2}})

Apply L'Hopital's Rule

: x \to 1 lim (\frac{7 a x ^{7 a - 1} - 7 a}{2 ( x - 1 )})

= x \to 1 lim (\frac{7 a x ^{7 a - 1} - 7 a}{2 ( x - 1 )})

Apply L'Hopital's Rule

: x \to 1 lim (\frac{7 a x ^{7 a - 2} ( 7 a - 1 )}{2})

= x \to 1 lim (\frac{7 a x ^{7 a - 2} ( 7 a - 1 )}{2})

Plug in the value

x = 1

= \frac{7 a \cdot 1 ^{7 a - 2} ( 7 a - 1 )}{2}

Simplify

= \frac{7 a ( 7 a - 1 )}{2}

\int \frac{1}{( x + 8 ) ^{2}} d x

\frac{d}{d x} (- y ln (x) - (1 - y) ln (1 - x))

x \to 1 + lim (x^{(\frac{1}{1 - x})})

\frac{\partial}{\partial x} (sin (x t))

\frac{d}{d x} (4 x - x^{2})

What is the limit as x approaches 1 of ((x^{7a}-7ax+7a-1))/((x-1)^2) ?
The limit as x approaches 1 of ((x^{7a}-7ax+7a-1))/((x-1)^2) is (7a(7a-1))/2