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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.

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¿Cuál de las siguientes funciones tiene limite 0 cuando \( x \) tiende a 2 ? \( \begin{array}{l}\text { a. } f(x)=\frac{x^{2}-4}{x-2} \\ \text { b. } f(x)=\frac{x^{2}-4}{x+2} \\ \text { c. } f(x)=\frac{1}{x-2} \\ \text { d. } f(x)=\frac{2}{x}\end{array} \) 5. \( P(x)=x^{4}-5 x-1 \) has a zero on which interval \( \begin{array}{lll}\text { a) }(0,1) & \text { b) }(1,2) & \text { c) }(2,3\end{array} \) 4. A tank contains 125 gallons of heating oil at \( t=0 \). During the interval \( 0 \leq t \leq 12 \) hours, heating oil is pumped into the tank at the rate \( H(t)=2+\frac{10}{(1+\ln (t+1))} \) gallons per hour. During the same time interval, heating oil is removed from the tank at the rate of \( R(t)=12 \sin \left(\frac{t^{2}}{47}\right) \) gallons per hour. Use your calculator to evaluate when necessary. a. How many gallons of heating oil are pumped into the tank during the time interval \( 0 \leq t \leq 12 \) hours? Show work. b. Is the level of heating oil in the tank rising or falling at \( t=6 \) hours? Show work. c. How many gallons of heating oil are in the tank at time \( t=12 \) hours? Show work. d. What is the average rate that oil is pumped out of the tank during the time interval \( 0 \leq t \leq 12 \). Show work. 2. The region \( R \) is bound by \( g(x)=0.3 x^{4}-2 x^{2}+1, h(x)=0.5 x-2 \) and the line \( x=0 \). Show a sketch the region \( R \) and determine the area with your calculator. Show integral. 2. The region \( R \) is bound by \( g(x)=0.3 x^{4}-2 x^{2}+1, h(x)=0.5 x-2 \) and the line \( x=0 \). Show a sketch the region \( R \) and determine the area with your calculator. Show integral. 2. The region \( R \) is bound by \( g(x)=0.3 x^{4}-2 x^{2}+1, h(x)=0.5 x-2 \) and the line \( x=0 \). Show a sketch the region \( R \) and determine the area with your calculator. Show integral. 2. The region \( R \) is bound by \( g(x)=0.3 x^{4}-2 x^{2}+1, h(x)=0.5 x-2 \) and the line \( x=0 \). Show a sketch the region \( R \) and determine the area with your calculator. Show integral. \( \int \frac { \omega t \pi x } { \cos \omega t x } + \frac { \phi \omega t x } { \sin x x t x } \) Exercice 1 Déterminer le développement limité en 0 à l'ordre \( n \) des fonctions suivantes : \( \quad \) 1. \( f(x)=\frac{e^{x}}{(1+x)^{3}} n=2 \) \( \int \frac { \omega t + \phi } { \sin x } + \frac { \pi \cos x t } { \omega t \phi } \)
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