Question

\(\lim\limits_{x\rightarrow1}\dfrac{x-5x^5+4x^6}{\left(1-x\right)^2}\)

Answer 1

\(\lim\limits_{x\rightarrow1}\dfrac{x-5x^5+4x^6}{\left(1-x\right)^2}=\lim\limits_{x\rightarrow1}\dfrac{x\left(1-5x^4+4x^5\right)}{\left(1-x\right)^2}\)

\(=\lim\limits_{x\rightarrow1}\dfrac{x\left(4x^5-8x^4+4x^3+3x^4-6x^3+3x^2+2x^3-4x^2+2x+x^2-2x+1\right)}{\left(1-x\right)^2}\)

\(=\lim\limits_{x\rightarrow1}\dfrac{x\left(x-1\right)^2\left(4x^3+3x^2+2x+1\right)}{\left(x-1\right)^2}\)

\(=\lim\limits_{x\rightarrow1}x\left(4x^3+3x^2+2x+1\right)=10\)

Answer 2

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