Let p - limx -2x-33x-54x-63x3 -2x2-x-1 and q - limx - 0-x2-5x-9 - x then the value of p - 2q is-

The correct option is C 2 p = lim_x →∞(2x 3)(3x+5)(4x 6)3x^3 +2x^2 x+1 = p = lim_x →∞x^3(2 3/x)(3+5/x)(4 6/x)x^3(3 +2/x 1/x^2+1/x^3=2× 3× 43=8 ...

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Single Point Continuity

Let p = lim...

Question

Let $p = {lim}_{x \to \infty} \frac{(2 x - 3) (3 x + 5) (4 x - 6)}{3 x^{3} + 2 x^{2} - x + 1}$ and $q = {lim}_{x \to 0} \sqrt{x^{2} - 5 x + 9} + x$ then the value of $p - 2 q$ is:

14

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2

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3

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\begin{matrix} {lim}_{x \to 1} \frac{x^{2} - 3 x + 2}{x^{2} - 4 x + 3} {lim}_{x \to 2} \frac{x^{3} + x^{2} - 12}{x^{3} - x^{2} - x - 2} {lim}_{x \to \sqrt{2}} \frac{x^{2} + x \sqrt{2} - 4}{x^{2} - 3 x \sqrt{2} + 4} {lim}_{x \to 3} \frac{x^{3} - 3 x^{2} - x + 3}{x^{3} - 6 x^{2} + 9 x} \end{matrix}

{lim}_{x \to 2} \frac{x^{2} - 5 x + 6}{x^{2} - x - 2} = \frac{- 1}{3}

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Evaluate the following one sided limits:

$(i) {lim}_{x \to 2^{+}} \frac{x - 3}{x^{2} - 4}$

$(i i) {lim}_{x \to 2^{-}} \frac{x - 3}{x^{2} - 4}$

$(i i i) {lim}_{x \to 0^{+}} \frac{1}{3 x}$

$(i v) {lim}_{x \to 8^{+}} \frac{2 x}{x + 8}$

$(v) {lim}_{x \to 0^{+}} \frac{2}{x^{\frac{1}{5}}}$

$(v i) {lim}_{x \to \frac{π^{-}}{2}} t a n x$

$(v i i) {lim}_{x \to \frac{π}{2^{+}}} s e c x$

$(v i i i) {lim}_{x \to 0^{-}} \frac{x^{2} - 3 x + 2}{x^{3} - 2 x^{2}}$

$(i x) {lim}_{x \to - 2^{+}} \frac{x^{2} - 1}{2 x + 4}$

$(x) {lim}_{x \to 0^{+}} (2 - c o t x)$

$(x i) {lim}_{x \to 0^{-}} 1 + c o s e c x$

lim x \to \infty f (x)

\frac{2 x - 3}{x} < f (x) < \frac{2 x^{2} + 5 x}{x^{2}}

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