_ n ( 3^n + 4^n )^ 1 n = - Vidyadip

MCQ

$\mathop {\lim }\limits_{n \to \infty } {({3^n} + {4^n})^{\frac{1}{n}}} = $

A
$3$
✓
$4$
C
$\infty $
D
$e$

✓

Answer

Correct option: B.

$4$

b
(b) $\mathop {{\rm{lim}}}\limits_{n \to \infty } \,{({3^n} + {4^n})^{\frac{1}{n}}}$

$ = \mathop {{\rm{lim}}}\limits_{n \to \infty } \,{({4^n})^{\frac{1}{n}}}{\left[ {\frac{{{3^n}}}{{{4^n}}} + 1} \right]^{\frac{1}{n}}}$

$ = \mathop {{\rm{lim}}}\limits_{n \to \infty } 4\,{\left[ {1 + \frac{1}{{{{\left( {\frac{4}{3}} \right)}^n}}}} \right]^{1/n}}$

$ = 4\mathop {{\rm{lim}}}\limits_{n \to \infty } \,{\left[ {1 + \frac{1}{{{{\left( {\frac{4}{3}} \right)}^n}}}} \right]^{1/n}}$

$ = 4{\left[ {1 + \frac{1}{\infty }} \right]^0} = 4 \times {(1)^0}$ $ = 4 \times 1 = 4$.

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 "M.C.Q (1 Marks)" from STD 11 - 12. limits→STD 11 - 12. limits — all question types→Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

A group of students comprises of $5$ boys and $n$ girls. If the number of ways, in which a team of $3$ students can randomly be selected from this group such that there is at least one boy and at least one girl in each team, is $1750$, then $n$ is equal to

All the letters of the word $"GTWENTY"$ are written in all possible ways with or without meaning and these words are written as in a dictionary. The serial number of the word $"GTWENTY"$ IS

There are $5$ students in class $10,6$ students in class $11$ and $8$ students in class $12.$ If the number of ways, in which $10$ students can be selected from them so as to include at least $2$ students from each class and at most $5$ students from the total $11$ students of class $10$ and $11$ is $100 \mathrm{k}$, then $\mathrm{k}$ is equal to $......$

Let $A = \{1, 2, 3\}$ and $B = \{2, 3, 4\}.$ Then which of the following is a function from $A$ to $B?$

If $\text{y}=\sqrt{\text{x}}+\frac{1}{\sqrt{\text{x}}},$ then $\frac{\text{dy}}{\text{dx}}$ at x = 1 is

A point $P$ moves on the line $2x -3y + 4 = 0$. If $Q(1, 4)$ and $R(3, -2)$ are fixed points, then the locus of the centroid of $\Delta PQR$ is a line

If $3$ is a root of ${x^2} + kx - 24 = 0,$ it is also a root of

The equation of the straight line passing through the point $(3, 2)$ and perpendicular to the line $y = x$ is:

If in the expansion of $\Big(\text{x}-\frac{1}{3\text{x}^{3}}\Big)^{9},$ the term independent of $x$ is:

If $\frac{\sqrt{2} \sin \alpha}{\sqrt{1+\cos 2 \alpha}}=\frac{1}{7}$ and $\sqrt{\frac{1-\cos 2 \beta}{2}}=\frac{1}{\sqrt{10}}$ $\alpha, \beta \in\left(0, \frac{\pi}{2}\right),$ then $\tan (\alpha+2 \beta)$ is equal to