I need to find the limit : lim n → ∞ 100 n + 25 + 6 n n

You could use the result often called the Squeeze Theorem. For large enough n (and it doesn't have to be very large!), we have 100 n + 25 + 6 n &lt; 2 ⋅ 6 n and therefore 6 &lt; 100 n + 25 + 6 n n &lt; 2 1 / n ( 6 ) .Now let n → ∞. As you mentioned, 2 1 / n → 1

Step by step solution to "I need to find the limit : lim..."

High School
Calculus and Analysis
Calculus 2
Series

Rapsinincke

Answered question

2022-07-05

I need to find the limit :

lim_{n \to \infty} \sqrt[n]{100 n + 25 + 6^{n}}

Answer & Explanation

Alexzander Bowman

Beginner2022-07-06Added 19 answers

You could use the result often called the Squeeze Theorem. For large enough n (and it doesn't have to be very large!), we have

100 n + 25 + 6^{n} < 2 \cdot 6^{n}

and therefore

6 < \sqrt[n]{100 n + 25 + 6^{n}} < 2^{1 / n} (6) .

Now let

n \to \infty

. As you mentioned,

2^{1 / n} \to 1

Do you have a similar question?

Recalculate according to your conditions!

New Questions in Calculus 2

What is the derivative of the work function?
How to use implicit differentiation to find $\frac{d y}{d x}$ given $3 x^{2} + 3 y^{2} = 2$ ?
How to differentiate $y = \log x^{2}$ ?
The solution of a differential equation y′′+3y′+2y=0 is of the form
A) $c_{1} e^{x} + c_{2} e^{2 x}$
B) $c_{1} e^{- x} + c_{2} e^{3 x}$
C) $c_{1} e^{- x} + c_{2} e^{- 2 x}$
D) $c_{1} e^{- 2 x} + c_{2} 2^{- x}$
How to find instantaneous velocity from a position vs. time graph?
How to implicitly differentiate $\sqrt{x y} = x - 2 y$ ?
What is 2xy differentiated implicitly?
How to find the sum of the infinite geometric series given $1 + \frac{2}{3} + \frac{4}{9} + ...$ ?
Look at this series: 1.5, 2.3, 3.1, 3.9, ... What number should come next?
A. 4.2
B. 4.4
C. 4.7
D. 5.1
What is the derivative of $\frac{x + 1}{y}$ ?
How to find the sum of the infinite geometric series 0.9 + 0.09 + 0.009 +…?
How to find the volume of a cone using an integral?
What is the surface area of the solid created by revolving $f (x) = e^{2 - x}, x \in [1, 2]$ around the x axis?
How to differentiate $x^{\frac{2}{3}} + y^{\frac{2}{3}} = 4$ ?
The differential coefficient of $\sec (\tan^{- 1} (x))$ .

Didn't find what you were looking for?