Download App

STD 11 - 12. limits — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 11 - 12. limits4 Marks
Question
$\mathop {\lim }\limits_{n \to \infty } {({4^n} + {5^n})^{1/n}}$ is equal to
✓

Answer

b
(b) Given limit $ = \mathop {\lim }\limits_{n \to \infty } \,{({4^n} + {5^n})^{1/n}}$

$ = \mathop {\lim }\limits_{n \to \infty } \,5\,{\left[ {{{\left\{ {1 + {{\left( {\frac{4}{5}} \right)}^n}} \right\}}^{{{(5/4)}^n}}}} \right]^{(1/n)\,.\,{{(4/5)}^n}}} = 5\,.\,{e^0} = 5$.

$\left( {\because \,\,{{\left( {\frac{4}{5}} \right)}^n} \to 0\,{\text{as }}\,n \to \infty } \right)$

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

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

If $\Delta (x) = \left| {\,\begin{array}{*{20}{c}}{{x^n}}&{\sin x}&{\cos x}\\{n!}&{\sin \frac{{n\pi }}{2}}&{\cos \frac{{n\pi }}{2}}\\a&{{a^2}}&{{a^3}}\end{array}\,} \right|,$ then the value of $\frac{{{d^n}}}{{d{x^n}}}[\Delta (x)]$ at $x = 0$ is
→
If $\smallint \frac{{5\tan x}}{{\tan x - 2\;}}dx$$ = x + aln\left| {\sin x - 2\cos x} \right| + k$ then $a $ is equal to
→
Given an $A.P.$ whose terms are all positive integers. The sum of its first nine terms is greater than $200$ and less than $220$. If the second term in it is $12$, then its $4^{th}$ term is
→
If $x\sin 45^\circ {\cos ^2}60^\circ = \frac{{{{\tan }^2}60^\circ {\rm{cosec}}30^\circ }}{{\sec 45^\circ {{\cot }^2}30^\circ }},$ then $x = $
→
Let.
$f(x)=\left\{\begin{array}{cc}3 x, & x<0 \\ \min \{1+x+[x], x+2[x]\}, & 0 \leq x \leq 2 \\ 5, & x>2\end{array}\right.$ where [.] denotes greatest integer function. If $\alpha$ and $\beta$ are the number of points, where f is not continuous and is not differentiable, respectively, then $\alpha+\beta$ equals
→
For any integer $k$ , let $w_k$ = $\cos \left( {\frac{{k\pi }}{{11}}} \right) + i\,\sin \left( { \frac{{k\pi }}{{11}}} \right)$ where $i$ = $\sqrt {-1}$ . The value of the expression $\frac{{\sum\limits_{k = 1}^8 {\left| {{w_{2k + 1}} - {w_{2k}}} \right|} }}{{\sum\limits_{k = 1}^4 {\left| {{w_{3k - 1}} - {w_{3k - 2}}} \right|} }}$ is
→
Let $a , b , c$ and $d$ be positive real numbers such that $a+b+c+d=11$. If the maximum value of $a^5 b^3 c^2 d$ is $3750 \beta$, then the value of $\beta$ is
→
If $[t]$ denotes the greatest integer $\leq t$, then number of points, at which the function $f ( x )=4|2 x +3|+$ $9\left[x+\frac{1}{2}\right]-12[x+20]$ is not differentiable in the open interval $(-20,20)$, is$.....$
→
If a tangent having slope of $ - \frac{4}{3}$ to the ellipse $\frac{{{x^2}}}{{18}} + \frac{{{y^2}}}{{32}} = 1$ intersects the major and minor axes in points $A$ and $B$ respectively, then the area of $\Delta OAB$ is equal to .................. $\mathrm{sq. \, units}$ ($O$ is centre of the ellipse)
→
If $\omega $ is a cube root of unity, then the value of ${(1 - \omega + {\omega ^2})^5} + {(1 + \omega - {\omega ^2})^5} = $
→