Calculus Archive: Questions from May 24, 2023
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10. Use the Laplace Transform to solve the IVP. \[ y^{\prime \prime}+y=\left\{\begin{array}{lr} t & , 0 \leq t2 answers -
Problema de optimizacion de Calculo III
Proyecto Math 1370: Nombre: Una compania contrata un ingeniero(a) para que diseñe una piscina de material plástico. inicialmente, elingeniero somete a la compañia undiseno preliminar como el que se0 answers -
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I. Determine la derivada (escoja 3 de los ejercicios) 1) \( f(x)=\arctan \left(e^{2 x}\right) \) 2) \( y=\frac{\operatorname{arcsen}(3 x)}{x} \) 3) \( y=\operatorname{sen}(\arccos (x)) \) 4) Determine2 answers -
II. Trabaje los integrales (escoja 3 de los ejercicios) 1) \( \int \frac{1}{x \sqrt{1-(\ln x)^{2}}} d x \) 2) \( \int \frac{\operatorname{sen}(x)}{4+\cos ^{2}(x)} d x \) 3) \( \int_{0}^{\sqrt{2}} \fra2 answers -
(1 point) Find \( y \) as a function of \( x \) if \[ y^{\prime \prime \prime}-4 y^{\prime \prime}+y^{\prime}-4 y=0 \text {, } \] \[ \begin{array}{l} y(0)=3 . \quad v^{\prime}(0)=-4 . \quad v^{\prime2 answers -
calculate the double integral
\( \iint_{R} \frac{x y^{2}}{x^{2}+1} d A, \quad R=\{(x, y) \mid 0 \leqslant x \leqslant 1,-3 \leqslant y \leqslant 3\} \)2 answers -
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HOMEWORK Q1: Differentiate: (1) \( y=2 x^{3}-7 x-\frac{2}{x^{2}}+1 \) (2) \( y=x^{5}-\frac{7}{x}+3 \sqrt{x}-2 \) (3) \( y=2 \sin 3 x-3 \csc 4 x \) (4) \( y=\frac{2}{\sqrt[3]{x^{2}-\cos x}} \) (5) \( y2 answers -
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