Login
Premium
Home Question Bank Math Calculus Archive 2024 December 18

Calculus Questions from Dec 18,2024

Browse the Calculus Q&A Archive for Dec 18,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

error msg
e. \( \lim _{n \rightarrow \infty}\left(\frac{n-2}{3 n+1}+\frac{6 n-1}{n+3}\right) \) Dplication : Dans chacun des cas suivants, déterminer une primitive de la fonction \( f \) sur l'intervalle \( I \). \( f(x)=2 x\left(x^{2}+1\right)^{4} \) et \( I=\mathbb{R} \). \( 2 f(x)=\frac{1}{(2 x-1)^{3}} \) et \( \left.I=\right] 1 ;+\infty[ \). (3) \( f(x)=\frac{\mathrm{e}^{3 x}}{\mathrm{e}^{3 x}+1} \) et \( I=\mathbb{R} \). xemple 11. Soit \( f \) la fonction définie sur \( \left[0,+\infty\left[\right.\right. \) par: \( f(x)=\left\{\begin{array}{ll}x^{1+\frac{1}{x}} & \text { si } x \neq 0 \\ 0 & \text { sinon }\end{array}\right. \). Montrer que \( f \) est continue en 0 \( f(x)=\ln x e d f(x)=x \ln x-x \) calcular dintegrade \( K=\int_{1}^{2} f(x) \) ret \( x \) - \( F(2)=2 \ln 2-2 \) ¿Cuál es el valor medio de \( f(x)=x^{3}+x^{2} \) en el intervalo \( \left[-\frac{2}{2}, 2\right] \) ? \( \begin{array}{l}\text { a. } 2.64 \\ \text { b. } 3.54 \\ \text { e. } 7.76 \\ \text { d. } 2.078\end{array} \) \( 5 . \int_{1}^{2} x^{2} \cdot d x \) Integrales Definidas \( \frac{\text { Exercice } \mathbf{1 1}}{\text { Soit les fonctions } f \text { et } g \text { définies par }} \) \( \left\{\begin{array}{r}f(x)=\frac{\sqrt{1+x^{2}}-1}{x} \\ f(0)=0\end{array}\right. \) si \( x \neq 0 \) et \( \mathrm{g}(x)=\left\{\begin{array}{c}\frac{x^{2}+x}{x+1} \text { si } x<-1 \\ x+\sqrt{x^{2}+3 x+2} \text { si } x \geq-1\end{array}\right. \) 1. Etudier la continuité et la dérivabilité de \( f \) en 0 ; interprét graphiquement le résultat. 2. a) Etudier la continuité et la dérivabilité de \( g \) sur son ensemb de définition. b) En déduire l'équation des deux demi-tangentes en -1 . Do all of the following question by showing all the necessary steps clearly and neatly. 1. Consider the sequence \( \left\{a_{n}\right\} \), where \( a_{1}=\sqrt{6}, a_{n+1}=\sqrt{6+a_{n}} \). Then (a) show that \( a_{n} \) is increasing and bounded. Utilice el teorema de Green para evaluar la integral \( \oint(y-x) d x+(2 x-y) d y \) donde C es la trayectoria que encierra la región \( y=x \) y \( y=x^{2}-2 x \). Verifique el resultado resolviendo la integral de línea mediante el método tradicional.
Prev 1 2 3 4 5 6
...
43 Next
1 2 3 4 5 6
...
43
Prev Next
Study can be a real struggle
Why not UpStudy it?
Select your plan below
Premium

You can enjoy

Start now
  • Step-by-step explanations
  • 24/7 expert live tutors
  • Unlimited number of questions
  • No interruptions
  • Full access to Answer and Solution
  • Full Access to PDF Chat, UpStudy Chat, Browsing Chat
Basic

Totally free but limited

  • Limited Solution
Welcome to UpStudy!
Please sign in to continue the Thoth AI Chat journey
Continue with Email
Or continue with
By clicking “Sign in”, you agree to our Terms of Use & Privacy Policy