Find the value of lim x- 0 xcos x -ln 1-x x 2

The correct option is B #160; 1 2 lim_x→ 0xcos x ln(1+x)x^2 =lim_x→ 0x(1 x^22!+.......) ( x x^22+....)x^2, (using series expansion ) =lim_ ...

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Right Hand Limit

Find the valu...

Question

Find the value of $lim x \to 0 \frac{x cos x - ln (1 + x)}{x^{2}}$

1

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\frac{1}{2}

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- \frac{1}{2}

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lim x \to 0 \frac{x cos x - log (1 + x)}{x^{2}}

Evaluate the following one sided limits:

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

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

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

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

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

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

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

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

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

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

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

i .

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i i i .

lim x \to 2 [\frac{x^{2} - 4}{x^{3} - 4 x^{2} + 4 x}]

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lim x \to 2 [\frac{x^{3} - 2 x^{2}}{x^{2} - 5 x + 6}]

v .

lim x \to 1 [\frac{x - 2}{x^{2} - x} - \frac{1}{x^{3} - 3 x^{2} + 2 x}]

lim x \to 1 {(\frac{x^{n} + x^{n - 1} + x^{n - 2} + . . . . + x^{2} + x - n}{x - 1})}

lim x \to 1 [{(\frac{4}{x^{2} - x^{- 1}} - \frac{1 - 3 x + x^{2}}{1 - x^{2}})}^{- 1} + 3 \frac{x^{4} - 1}{x^{3} - x^{- 1}}] .

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