Download App

Limits — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsLimits3 Marks
Question
Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow{\text{a}}}\frac{(\text{x}+2)^{\frac{5}{2}}-(\text{a}+2)^{\frac{5}{2}}}{\text{x}-\text{a}}$
✓

Answer

$\lim\limits_{\text{x}\rightarrow{\text{a}}}\frac{(\text{x}+2)^{\frac{5}{2}}-(\text{a}+2)^{\frac{5}{2}}}{\text{x}-\text{a}}$$=\lim\limits_{\text{x}\rightarrow{\text{a}}}\frac{(\text{x}+2)^{\frac{5}{2}}-(\text{a}+2)^{\frac{5}{2}}}{(\text{x}+2)-(\text{a}+2)}$
$=\lim\limits_{\text{y}\rightarrow{\text{b}}}\frac{\text{y}^\frac{5}{2}-\text{b}^\frac{5}{2}}{\text{y}-\text{b}},$ where x + 2 = y and a + 2 = b
$=\frac{5}{2}\text{b}^{\frac{5}{2}-1}$ $\Big[\text{Using formula}\ \lim\limits_{\text{x}\rightarrow{\text{a}}}\frac{\text{x}^{\text{n}}-\text{a}^\text{n}}{\text{x}-\text{a}}=\text{na}^{\text{n}-1}\Big]$
$=\frac{5}{2}(\text{a}+2)^{\frac{5}{2}-1}$
$=\frac{5}{2}(\text{a}+2)^{\frac{3}{2}}$

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.(3 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

Evaluate the following one sided limits:
$\lim\limits_{\text{x}\rightarrow0^-}(2-\cos\text{x})$
→
Evaluate the following limits: $\lim _{x \rightarrow 3}\left[\frac{1}{x-3}-\frac{9 x}{x^3-27}\right]$
→
In the following expansions, find the indicated coefficients.

$x ^3$ in $\left(x^2+\frac{3 \sqrt{2}}{x}\right)^9$

→
Find the values of x and y which satisfy the following equations (x, y ∈ R)

If $x(1+3 i)+y(2-i)-5+i^3=0$, find $x+y$

→
If a, b, c are in A.P. and a, b, d are in G.P., show that a, (a - b), (d - c) are in G.P.
→
Let A = {x : x $\in$ N}, B = {x : x = 2n, n $\in$ N}, C = {x : x = 2n - 1, n $\in$ N} and D = {x : x is a prime natural number}. Find:
$\text{A}\cap\text{B}$
→
Find all pairs of consecutive odd natural number, both of which are larger than 10, such that their sum is less than 40.
→
Solve the following equation:
$4\sin^{2}\text{x}-8\cos\text{x}+1=0$
→
The radius of a circle is 30cm. Find the length of an arc of this circle, if the length of the chord of the arc is 30cm.
→
Find the magnitude, in radians and degrees, of the interior angle of a regular.
Pentagon
→