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Home Question Bank Math Calculus Archive 2024 December 22

Calculus Questions from Dec 22,2024

Browse the Calculus Q&A Archive for Dec 22,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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Hallar los puntos (si los hay) en que no sea continua la función: \[ =\frac{|X|}{X} \] a. No es continua en \( x=0 \) b. No es continua en \( x=1 \) c. Es continua para todos los valores de \( x \). d. No es continua en \( x=3 \) La función es continua en el punto dado: \( f_{1}(x)=\left\{\begin{array}{ll}|x| & : x<2 \\ 2 x-3 & : \text { en caso contrario }\end{array}\right. \) Verdadero Falso Hallar los puntos (si los hay) en que no sea continua la función: COS X a. WNo es continua en \( x=0 \) b. No es continua en \( x=1 \) c. Es continua para todos los valores de x . d. No es continua en \( x=3 \) ¿Cuál de las siguientes funciones \( f \) tiene una discontinuidad removible en \( a \) ? Si la discontinuidad es removible, halle una función \( g \) que concuerde con \( f \) para \( x \neq a \) y sea continua en \( a \). (a) \( f(x)=\frac{x^{4}-1}{x-1}, a=1 \) (b) \( f(x)=\frac{x^{3}-x^{2}-2 x}{x-2}, a=2 \) (c) \( f(x)=\llbracket \operatorname{sen} x \rrbracket, a=\pi \) a. ayc b. ayb c. Solamente a. d. byc The volume of a cylindrical tank needs to be 500 liters. How can you determine the radius and height that minimize the material required for the tank's construction? \( \int \frac { \sqrt { 529 - 4 x ^ { 2 } } } { 4 x ^ { 2 } } d x \) اعثر على حجم الجسم الناتج عن دوران المنحنى \( y = 5 - x^{2} \) حول المحور العمودي عند \( x = 6 \). Express the given integrand as a sum of partial fractions the integrals. \( \int_{1 / 2}^{1} \frac{3 y+4}{y^{2}+y} d y \) Express the integrand as a sum of partial fractions and evaluate the integral. \( \int_{8}^{13} \frac{y}{y^{2}-4 y-5} d y \) \( \int \frac { \sqrt { 529 - 4 x ^ { 2 } } } { 4 x ^ { 2 } } d x \)
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