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Black Advanced Problems in Mathematics

Exam: Black Advanced Problems in Mathematics
Subject: Mathematics
Chapter: Indefinite and Definite Integration

Black Advanced Problems in Mathematics · Mathematics · Indefinite and Definite Integration

Let l_1 = _ x → ∞ (x - ^2 x)/(x + x) and l_2 = _ h → 0^+ ∫_ -1 ^1...

Let

l_1 = \lim_{x \to \infty} \frac{x - \cos^2 x}{x + \sin x}

and

l_2 = \lim_{h \to 0^+} \int_{-1}^1 \frac{h dx}{h^2 + x^2}

. Then :

Options

ABoth $l_1$ and $l_2$ are less than 22/7
BOne of the two limits is rational and other irrational
C $l_2 > l_1$
D $l_2$ is greater than 3 times of $l_1$

Correct answer

A. Both $l_1$ and $l_2$ are less than 22/7

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