Using L'Hospital's rule, evaluate: lim(x→0) (xe^x − log(1+x))/x²

Question

TextLeft Hand and Right Hand Limits

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Find lim[x→0] f(x) and lim[x→1] f(x), where f(x) = { 2x+3, x ≤ 0; 3(x+1), x > 0 }

Find lim[x→1] f(x), where f(x) = { x²-1, x ≤ 1; -x²-1, x > 1 }

Evaluate lim[x→0] f(x), where f(x) = { |x|/x, x ≠ 0; 0, x = 0 }

TextLeft Hand and Right Hand Limits

Find lim[x→0] f(x), where f(x) = { x/|x|, x ≠ 0; 0, x = 0 }

Find lim[x→5] f(x), where f(x) = |x| - 5

Suppose f(x) = { a+bx, x < 1; 4, x = 1; b-ax, x > 1 } and if lim[x→1] f(x) = f(1) what are possible values of a and b?