b,
\(\overset{lim}{x\rightarrow1}\dfrac{4x^6-5x^5+x}{\left(1-x\right)^2}=\overset{lim}{x\rightarrow1}\dfrac{\left(4x^5-4x^2-x^4+1\right)x}{\left(1-x\right)^2}\)
\(=lim_{x\rightarrow1}\dfrac{\left[4x^4\left(x-1\right)-\left(x^2-1\right)\left(x^2+1\right)\right]x}{\left(1-x\right)^2}\)
\(=lim_{x->1}\dfrac{x\left(x-1\right)\left[4x^4-\left(x+1\right)\left(x^2+1\right)\right]}{\left(x-1\right)^2}=lim_{x->1}\dfrac{x\left(4x^4-x^3-x^2-x-1\right)}{x-1}\)
\(=lim_{x->1}\dfrac{x\left(x-1\right)\left(4x^3+3x^2+2x+1\right)}{x-1}\)
\(=limx(4x^3+3x^2+2x+1)=4+3+2+1=10\)
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