Lim x - 0x3 x-1-cos x-AI CBSE - DSSE 1988-

The correct option is C 2 lim_x→ 0 (x^3cot x)/1 cos x = lim_x→ 0 (x^3 cot x/1 cos x × 1+ cos x/1+ cos x) = lim_x→ 0 (x/sin x)^3 × lim_x→ 0 cosx × lim_x→ 0 (1+c ...

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Byju's Answer

Standard XI

Mathematics

Standard Limits to Remove Indeterminate Form

lim x → 0x3 x...

Question

$l i m_{x \to 0}$ $\frac{(x^{3} c o t x)}{1 - c o s x}$ =

[AI CBSE ; DSSE 1988]

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Solution

The correct option is C
2

$l i m_{x \to 0}$ $\frac{(x^{3} c o t x)}{1 - c o s x}$
= $l i m_{x \to 0}$ ( $\frac{x^{3} c o t x}{1 - c o s x}$ × $\frac{1 + c o s x}{1 + c o s x}$ )
= $l i m_{x \to 0}$ ${(\frac{x}{s i n x})}^{3}$ × $l i m_{x \to 0}$ cosx × $l i m_{x \to 0}$ (1+cos x) =2

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Similar questions

$l i m_{x \to 0}$ $\frac{(x^{3} c o t x)}{1 - c o s x}$ =

[AI CBSE ; DSSE 1988]

${lim}_{x \to 0} \frac{x^{3} c o t x}{1 - c o s x}$

lim x \to 0 \frac{x^{3} cot x}{1 - cos x} = ?

Q. Solve

lim x \to 0 \frac{x^{3} cot x}{1 - cos x}

Q. Find the following limit:

lim x \to 0 x cot 3 x

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limx→0 (x3cotx)1−cosx = [AI CBSE ; DSSE 1988]

The correct option is C 2 limx→0 (x3cotx)1−cosx = limx→0 (x3cotx1−cosx × 1+cosx1+cosx) = limx→0 (xsinx)3 × limx→0 cosx × limx→0 (1+cos x) =2

$l i m_{x \to 0}$ $\frac{(x^{3} c o t x)}{1 - c o s x}$ =

[AI CBSE ; DSSE 1988]

The correct option is C
2

$l i m_{x \to 0}$ $\frac{(x^{3} c o t x)}{1 - c o s x}$
= $l i m_{x \to 0}$ ( $\frac{x^{3} c o t x}{1 - c o s x}$ × $\frac{1 + c o s x}{1 + c o s x}$ )
= $l i m_{x \to 0}$ ${(\frac{x}{s i n x})}^{3}$ × $l i m_{x \to 0}$ cosx × $l i m_{x \to 0}$ (1+cos x) =2