Evaluate: $\lim_{x \to \infty}$ $\sqrt{x}$ ($\root3 \of{x+1}$ - $ \root3 \of{x-1})$
I tried to multip. by the conjugate, but it just turned into a big mess with nowhere to go
2026-04-02 23:33:41.1775172821
Limit involving cube root
88 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in LIMITS
- How to prove $\lim_{n \rightarrow\infty} e^{-n}\sum_{k=0}^{n}\frac{n^k}{k!} = \frac{1}{2}$?
- limit points at infinity
- Calculating the radius of convergence for $\sum _{n=1}^{\infty}\frac{\left(\sqrt{ n^2+n}-\sqrt{n^2+1}\right)^n}{n^2}z^n$
- Maximal interval of existence of the IVP
- Divergence of power series at the edge
- Compute $\lim_{x\to 1^+} \lim_{n\to\infty}\frac{\ln(n!)}{n^x} $
- why can we expand an expandable function for infinite?
- Infinite surds on a number
- Show that f(x) = 2a + 3b is continuous where a and b are constants
- If $a_{1}>2$and $a_{n+1}=a_{n}^{2}-2$ then Find $\sum_{n=1}^{\infty}$ $\frac{1}{a_{1}a_{2}......a_{n}}$
Related Questions in LIMITS-WITHOUT-LHOPITAL
- Solving a limit of $\frac{\ln(x)}{x-1}$ with taylor expansion
- Limit of $\sqrt x \sin(1/x)$ where $x$ approaches positive infinity
- No two sided limit exists
- Evaluate $\lim\limits_{n\to\infty} \frac{3+\sqrt{3}+\sqrt[3]{3}+\dots+\sqrt[n]{3}-n}{\ln n}$
- A problem in using theorem for finding limit
- A guess about sequences
- Compute the limit without L'Hospital's rule
- $x_0 \in [0,\infty)$ and $x_{n+1} =\sqrt{\frac{3x_n+2}{2}}$. Compute $\lim_\limits{n\to\infty} x_n$
- Substitution in the limit $x^{2}\sin(\frac{1}{x})$ where $x \to \infty$
- Evaluate $\lim_{ x\to \infty} x^2 \times \log \left(x \cot^{-1}x\right)$
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?
HINT
$$\root3 \of{x+1} - \root3 \of{x-1} \frac{\sqrt[3]{(x+1)^2}+ \sqrt[3]{x^2-1}+\sqrt[3]{(x-1)^2}}{\sqrt[3]{(x+1)^2}+ \sqrt[3]{x^2-1}+\sqrt[3]{(x-1)^2}}$$