I know that from $$e^x=\sum_{i=0}^\infty \left(\frac{x^i}{i!}\right)$$ we can get the inequality $e^x\ge1+x$. But how?
2025-04-21 22:05:13.1745273113
How to use Taylor series to get $e^x\geq1+x$
111 Views Asked by Weronika Gorycka https://math.techqa.club/user/weronika-gorycka/detail AtRelated Questions in CALCULUS
- Derivative of Lambert W function.
- how to use epsilion-delta limit definition to answer the following question?
- Finding the equation of a Normal line
- How to Integrate the Differential Equation for the Pendulum Problem
- Help in finding error in derivative quotient rule
- How to solve the following parabolic pde?
- Finding inflection point
- How to find the absolute maximum of $f(x) = (\sin 2\theta)^2 (1+\cos 2\theta)$ for $0 \le \theta \le \frac{\pi}2$?
- Utility Maximization with a transformed min function
- Interpreting function notation?
Related Questions in EXPONENTIAL-FUNCTION
- Simply this exponential integral
- Inverse Laplace transform of $\frac{r_1e^{-t_0s}}{s + r_2 + r_3}$
- Solving a pair of kinetic equations using the Laplace transform
- Algebra: logarithms word question
- Exponential r.v.s. problem
- Simplify an exponential integral
- Finding number pattern
- For which orthogonal matrices does the matrix exponential converge?
- Analytic Function with Exponential Coefficients
- Euler's derivation of e?
Related Questions in TAYLOR-EXPANSION
- Asymptotic expansion for the solution of linear KDV eq.
- Find limit using Maclaurin series (remember the importance of big O notation)
- Evaluate the following limit using Taylor series.
- How can we show that $\sum\limits_{n=1}^\infty |c_n| < \infty$ when $c_n$ is taylor series coefficients of $f(z): \mathbb{C} \rightarrow \mathbb{C}$?
- terms of taylor expansions of multiple variables at the origin
- Convergence radius of $\sum_{n=1}^\infty (-1)^nn^nx^{n^2} $
- Finding the explicit sum of $ \sum_{n=1}^\infty n(n+1)(\frac{1}{2})^n $
- If $0<|z|<1$, show that $\frac{1}{4}|z|<|1-e^z|<\frac{7}{4}|z|$
- Series solution of an ODE (taylor series, infinite series)
- Approximation of non-analytic function
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Refuting the Anti-Cantor Cranks
- Find $E[XY|Y+Z=1 ]$
- 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?
- What are the Implications of having VΩ as a model for a theory?
- How do we know that the number $1$ is not equal to the number $-1$?
- Defining a Galois Field based on primitive element versus polynomial?
- Is computer science a branch of mathematics?
- Can't find the relationship between two columns of numbers. Please Help
- 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
- A community project: prove (or disprove) that $\sum_{n\geq 1}\frac{\sin(2^n)}{n}$ is convergent
- Alternative way of expressing a quantied statement with "Some"
Popular # Hahtags
real-analysis
calculus
linear-algebra
probability
abstract-algebra
integration
sequences-and-series
combinatorics
general-topology
matrices
functional-analysis
complex-analysis
geometry
group-theory
algebra-precalculus
probability-theory
ordinary-differential-equations
limits
analysis
number-theory
measure-theory
elementary-number-theory
statistics
multivariable-calculus
functions
derivatives
discrete-mathematics
differential-geometry
inequality
trigonometry
Popular Questions
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- How to find mean and median from histogram
- Difference between "≈", "≃", and "≅"
- Easy way of memorizing values of sine, cosine, and tangent
- How to calculate the intersection of two planes?
- What does "∈" mean?
- If you roll a fair six sided die twice, what's the probability that you get the same number both times?
- Probability of getting exactly 2 heads in 3 coins tossed with order not important?
- Fourier transform for dummies
- Limit of $(1+ x/n)^n$ when $n$ tends to infinity