Find the left and right hand limits of fx- 3x2-23x-2 x1 - at x-1

$(i) \frac{1}{3} x - 6 = \frac{5}{2} (i i) \frac{2 x}{3} - \frac{3 x}{8} = \frac{7}{12} (i i i) (x + 2) (x + 3) + (x - 3) (x - 2) - 2 x (x + 1) = 0 (i v) \frac{1}{10} - \frac{7}{x} = 35 (v) 13 (x - 4) - 3 (x - 9) - 4 (x + 4) = 0 (v i) x + 7 - \frac{8 x}{3} = \frac{17 x}{6} - \frac{5 x}{8} (v i i) \frac{3 x - 2}{4} - \frac{2 x + 3}{3} = \frac{2}{3} - x (v i i i) \frac{x + 2}{6} - (\frac{11 - x}{3} - \frac{1}{4}) = \frac{3 x - 4}{12} (i x) \frac{2}{5 x} - \frac{5}{3 x} = \frac{1}{15} (x) \frac{x + 2}{3} - \frac{x + 1}{5} = \frac{x - 3}{4} - 1 (x i) \frac{3 x - 2}{3} + \frac{2 x + 3}{2} = x + \frac{7}{6} (x i i) x - \frac{x - 1}{2} = 1 - \frac{x - 2}{3} (x i i i) \frac{9 x + 7}{2} - (x - \frac{x - 2}{7}) = 36 (x i v) \frac{6 x + 1}{2} + 1 = \frac{7 x - 3}{3}$

Question 2
Which of the following is not a quadratic equation?
(a) $2 (x - 1)^{2} = 4 x^{2} - 2 x + 1$
(b) $2 x - x^{2} = x^{2} + 5$
(c) ${(\sqrt{2} x + \sqrt{3})}^{2} = 3 x^{2} - 5 x$
(d) $(x^{2} + 2 x)^{2} = x^{4} + 3 + 4 x^{3}$

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Find the left and right hand limits of f(x)=⎧⎪ ⎪ ⎪⎨⎪ ⎪ ⎪⎩3x2+23x−2x<14x2−34x+3x>1 at x=1

The correct option is A (a) 5 and 17f(x)=⎧⎪ ⎪ ⎪⎨⎪ ⎪ ⎪⎩3x2+23x−2x<14x2−34x+3x>1Limx→1−f(x)=3x2+23x−2=3(1)+23(1)−2=3+23−2=5Limx→1+f(x)=4x2−34x+3=4(1)−34(1)+3=17

Find the left and right hand limits of $f (x) = ⎧ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎩ \begin{matrix} \frac{3 x^{2} + 2}{3 x - 2} x < 1 \frac{4 x^{2} - 3}{4 x + 3} x > 1 \end{matrix}$ at $x = 1$