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Integration by Substitution

If l=lim x→...

Question

If $l = lim x \to 0 \frac{x (1 + a cos x) - b sin x}{x^{3}}$ if limit is finite then find relation between a and b.

b=a+1

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a

and

b

are any real numbers

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a = 0

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a = 0, b = 2

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Solution

The correct option is A b=a+1

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Similar questions

a

b

{lim}_{x \leftarrow 0} \frac{x (1 + a cos x) - b sin x}{x^{3}} = 1

f (x)

{lim}_{x \to 0} \frac{f (x)}{x} = 1

{lim}_{x \to 0} \frac{x (1 + a cos x) - b sin x}{{f (x)}^{3}} = 1

| a + b | =

l = {lim}_{x \to 0} \frac{x (1 + a c o s x) - b s i n x}{x^{3}}

l \in R

f (x) = ⎧ ⎨ ⎩ \begin{matrix} \frac{x (1 + a cos x) - b sin x}{x^{3}}, x \neq 0 1, x = 0 \end{matrix}

f

a

b

lim x \to 0 \frac{x (1 + a cos x) - b sin x}{x^{3}} = 1

a, b

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