Download App

Limits — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsLimits4 Marks
Question
Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow3}\frac{\text{x}-3}{\sqrt{\text{x}-2}-\sqrt{4-\text{x}}}$
✓

Answer

$\lim\limits_{\text{x}\rightarrow3}\frac{\text{x}-3}{\sqrt{\text{x}-2}-\sqrt{4-\text{x}}}$$=\lim\limits_{\text{x}\rightarrow3}\frac{\text{x}-3}{\big(\sqrt{\text{x}-2}-\sqrt{4-\text{x}}\big)}\times\frac{\big(\sqrt{\text{x}}-2+\sqrt{4-\text{x}}\big)}{\big(\sqrt{\text{x}}-2+\sqrt{4-\text{x}}\big)}$
$=\lim\limits_{\text{x}\rightarrow3}\frac{(\text{x}-3)\big(\sqrt{\text{x}-2}+\sqrt{4-\text{x}}\big)}{(\text{x}-2)-(4-\text{x})}$
$=\lim\limits_{\text{x}\rightarrow3}\frac{(\text{x}-3)\big(\sqrt{\text{x}-2}+\sqrt{4-\text{x}}\big)}{\text{x}-2-4+\text{x}}$
$=\lim\limits_{\text{x}\rightarrow3}\frac{(\text{x}-3)\big(\sqrt{\text{x}-2}+\sqrt{4-\text{x}}\big)}{2(\text{x}-3)}$
$=\frac{1}{2}\lim\limits_{\text{x}\rightarrow3}\big(\sqrt{\text{x}-2}+\sqrt{4-\text{x}}\big)$
$=\frac{1}{2}\big(\sqrt{3-2}+\sqrt{4-\text{x}}\big)$
$=\frac{1}{2}\big(\sqrt{1}+\sqrt{1}\big)$
$=\frac{1}{2}(1+1)=\frac22$
$=1$

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 "Solve the Following Question.(4 Marks)" from Limits→Limits — all question types→Maths STD 11 Science question papers→Maharashtra Board STD 11 Science question papers→Maharashtra Board question paper generator→

Similar questions

If $\Big(\frac{1+\text{i}}{1-\text{i}}\Big)^3-\Big(\frac{1-\text{i}}{1+\text{i}}\Big)^3=\text{x}+\text{iy,}$ find (x, y)
→
Let r and n be positive integers such that 1 < r < n. Then prove the following:
${^\text{n}\text{C}}_{\text{r}}+2\ {^\text{n}\text{C}}_{\text{r}-1}+{^\text{n}\text{C}}_{\text{r}-2}={^\text{n+2}\text{C}}_{\text{r}}$
→
Find the cartesian co-ordinates of the points on the parabola $y^2=12 x$ whose parameters are $: 1.2 2.-3$
→
In each of the following find the equations of the hyperbola satisfying the given conditions:Vertices $(\pm2, 0)$, foci $(\pm3, 0)$ [NCERT]
→
Find the angle in radians through which a pendulum swings if its length is 75cm and the tip describes an arc of length.
  1. 10cm
  2. 15cm
  3. 21cm
→
Find $m$ and $n$, if ${ }^{(m+n)} P_2=56$ and ${ }^{(m-n)} P_2=12$.
→
Find the square roots of
3 – 4i
→
From 4 officers and 8 jawans in how many ways can 6 be chosen:
  1. To include exactly one officer.
  2. To include at least one officer?
→
Find the derivatives of the following w.r.t. x by using the method of the first principle.

sec(5x – 2)

→
Find the equation of the line passing through the point of intersection of the lines 4x - 7y - 3 = 0 and 2x - 3y + 1 = 0 that has equal intercepts on the axes.
→