Arrange the following limits in the ascending order of their values1 limx - 1-x2-x x-22 limx - 0 1-2x 3-x3 lim- 0 sin-2- 4 limx - 0ln 1-xx

Using standard formulae (1) e^lim_x →∞(2+x) ( 1+x 2 x2+x ) =e^ 1=1e (2) e^lim_x → 03x(1+2x 1)=e^6 (3) lim_x → 0sinθθ . 12=12 (4) lim_x → 0ln (1+x)x=1 ...

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Standard XII

Mathematics

Single Point Continuity

Arrange the f...

Question

Arrange the following limits in the ascending order of their values
$(1) lim x \to \infty {(\frac{1 + x}{2 + x})}^{x + 2}$
$(2) lim x \to 0 {(1 + 2 x)}^{3 / x}$
$(3) lim θ \to 0 (\frac{sin θ}{2 θ})$
$(4) lim x \to 0 \frac{ln (1 + x)}{x}$

1, 2, 3, 4

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1, 3, 4, 2

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1, 4, 3, 2

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3, 4, 1, 2

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Solution

The correct option is B $1, 3, 4, 2$
Using standard formulae
$(1) e^{lim x \to \infty (2 + x) ⎛ ⎝ \frac{1 + x - 2 - x}{2 + x} ⎞ ⎠} = e^{- 1} = \frac{1}{e}$
$(2) e^{lim x \to 0 \frac{3}{x} (1 + 2 x - 1)} = e^{6}$
$(3) lim x \to 0 \frac{sin θ}{θ} . \frac{1}{2} = \frac{1}{2}$
$(4) lim x \to 0 \frac{ln (1 + x)}{x} = 1$

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Single Point Continuity

Standard XII Mathematics

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Arrange the following limits in the ascending order of their values (1) limx→∞(1+x2+x)x+2 (2) limx→0(1+2x)3/x (3) limθ→0(sinθ2θ) (4) limx→0ln(1+x)x

The correct option is B 1,3,4,2Using standard formulae (1) elimx→∞(2+x)⎛⎝1+x−2−x2+x⎞⎠=e−1=1e (2) elimx→03x(1+2x−1)=e6 (3) limx→0sinθθ.12=12 (4) limx→0ln(1+x)x=1

Arrange the following limits in the ascending order of their values
$(1) lim x \to \infty {(\frac{1 + x}{2 + x})}^{x + 2}$
$(2) lim x \to 0 {(1 + 2 x)}^{3 / x}$
$(3) lim θ \to 0 (\frac{sin θ}{2 θ})$
$(4) lim x \to 0 \frac{ln (1 + x)}{x}$