Show that _ x 2^- x [x] _ x 2^+ x [a] .

Question

Show that $\lim\limits_{\text{x}\rightarrow2^-}\ \frac{\text{x}}{[\text{x}]}\ne\lim\limits_{\text{x}\rightarrow2^+}\frac{\text{x}}{[\text{a}]}.$

✓

Answer

$\lim\limits_{\text{x}\rightarrow2^-}\ \frac{\text{x}}{[\text{x}]}$ $=\lim\limits_{\text{x}\rightarrow2^-}\ \frac{\text{x}}{1}=\frac{2}{1}=2$ $\bigg[\because\lim\limits_{\text{x}\rightarrow\text{k}^-}\ [\text{x}]=\text{k}-1\bigg]$ Also, $\lim\limits_{\text{x}\rightarrow2^+}\frac{\text{x}}{[\text{x}]}=\lim\limits_{\text{x}\rightarrow2^-}\frac{\text{x}}{3}=\frac23$ $\bigg[\because\lim\limits_{\text{x}\rightarrow\text{k}^+}\ [\text{x}]=\text{k}+1\bigg]$ $\Rightarrow\lim\limits_{\text{x}\rightarrow2^-}\ \frac{\text{x}}{[\text{x}]}\ne\lim\limits_{\text{x}\rightarrow2^+}\frac{\text{x}}{[\text{x}]}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "(Each question 3 marks)" from Limits→Limits — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Limits — MATHS STD 11 Science — Question

Answer

Need a full question paper?

Explore more

Similar questions