Evaluate i lim x - 3x2-9-x-3ii lim x - 1x2-4 x-3-x-1

(i) x→3lim ( x^2 9/x 3 )x → 3lim(x+3)(x 3)/(x 3)=x → 3lim(x+3)=6 (ii) x→1lim ( (x^2 4x+3)/x 1 ) x → 3lim(x 1)(x 3)/(x 1)=x → 3lim(x 3)= 2 Rule III If the giv ...

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Standard XI

Mathematics

Logarithmic Inequalities

Evaluate i li...

Question

Evaluate (i) $l i m x \to 3 (\frac{x^{2} - 9}{x - 3})$

(ii) $l i m x \to 1 (\frac{(x^{2} - 4 x + 3)}{x - 1})$

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Solution

(i) $l i m x \to 3 (\frac{x^{2} - 9}{x - 3}) l i m x \to 3 \frac{(x + 3) (x - 3)}{(x - 3)} = l i m x \to 3 (x + 3) = 6$

(ii) $l i m x \to 1 (\frac{(x^{2} - 4 x + 3)}{x - 1}) l i m x \to 3 \frac{(x - 1) (x - 3)}{(x - 1)} = l i m x \to 3 (x - 3) = - 2$

Rule III If the given function contains a surd them simplify it by using conjugate surds. After simplification, put x=a.

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Evaluate (i) limx→3(x2−9x−3) (ii) limx→1((x2−4x+3)x−1)

(i) limx→3(x2−9x−3)limx→3(x+3)(x−3)(x−3)=limx→3(x+3)=6 (ii) limx→1((x2−4x+3)x−1)limx→3(x−1)(x−3)(x−1)=limx→3(x−3)=−2 Rule III If the given function contains a surd them simplify it by using conjugate surds. After simplification, put x=a.

Evaluate (i) $l i m x \to 3 (\frac{x^{2} - 9}{x - 3})$

(ii) $l i m x \to 1 (\frac{(x^{2} - 4 x + 3)}{x - 1})$