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DPP 07 — Limits

JEE Main · MathsTime: 15 minMax marks: 16

Evaluate

\lim\limits_{x \to 0} \dfrac{\sin 3x}{x}

(A)

0

(B)

1

(C)

3

(D)

\infty

\lim\limits_{x \to 0} \dfrac{1 - \cos x}{x^{2}}

equals

(A)

0

(B)

\dfrac{1}{2}

(C)

1

(D)

2

\lim\limits_{x \to \infty} \left(1 + \dfrac{2}{x}\right)^{x}

equals

(A)

e

(B)

e^{2}

(C)

2

(D)

1

\lim\limits_{x \to 0} \dfrac{\sin x - x}{x^{3}}

equals

(A)

\dfrac{1}{6}

(B)

-\dfrac{1}{6}

(C)

0

(D)

-\dfrac{1}{3}

Answer key1-C2-B3-B4-B

GRAPH

y = \dfrac{\sin x}{x}

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✓ JEE Main · Maths ✓ Limits

✓ Saved on this device

\lim\limits_{x \to 0} \frac{\sin x}{x} = 1

v^{2} = u^{2} + 2as

\mathrm{pH} = -\log[\mathrm{H^{+}}]

\int_{0}^{\pi} \sin x \, dx = 2

K_{p} = K_{c}(RT)^{\Delta n}

f^{-1}(f(x)) = x

PV = nRT

\frac{d}{dx}\left(x^{n}\right) = nx^{n-1}

\Delta G = \Delta H - T\Delta S

F = ma

e^{i\pi} + 1 = 0

s = ut + \frac{1}{2}at^{2}

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✓ Limits DPP · 15 Qs Auto-pick ✓

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Daily practice — Limits

Evaluate

\lim\limits_{x \to 0} \dfrac{\sin 3x}{x}

\lim\limits_{x \to 0} \dfrac{1 - \cos x}{x^{2}}

equals

\lim\limits_{x \to \infty} \left(1 + \dfrac{2}{x}\right)^{x}

equals

\lim\limits_{x \to 0} \dfrac{\sin x - x}{x^{3}}

equals

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Practice sheet — Limits

JEE Main · 1 chapterTime: 6 minMax marks: 8

Evaluate

\lim\limits_{x \to 0} \dfrac{\sin 3x}{x}

(A)

0

(B)

1

(C)

3

(D)

\infty

\lim\limits_{x \to \infty} \left(1 + \dfrac{2}{x}\right)^{x}

equals

(A)

e

(B)

e^{2}

(C)

2

(D)

1

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