Calculus Archive: Questions from May 16, 2023
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Compute the second-order partial derivatives of \[ \begin{array}{l} f(x, y)=e^{5 x^{2}+4 y^{2}} \\ \frac{\partial^{2} f}{\partial x^{2}}(x, y)= \\ \frac{\partial^{2} f}{\partial x \partial y}(x, y)=[2 answers -
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\( \begin{array}{l}\text { Evaluate } \int_{C} \mathbf{F} \cdot d \mathbf{r} \\ \qquad \begin{array}{l} \mathbf{F}(x, y)=x \mathbf{i}+y \mathbf{j} \\ C: \mathbf{r}(t)=(9 t+1) \mathbf{i}+t \mathbf{j},2 answers -
I. Evalúe \( \int_{c} F \cdot d r \) donde \( C \) está representada por \( r(t) \). a) \( F(x, y)=3 x i+4 y j ; C: r(t)=\cos (t) i+\operatorname{sen}(t) j \) donde \( 0 \leq t \leq \pi / 2 \)2 answers -
Differentiate the function. y' y = 7√1-x3 6
Differentiate the function. \[ y=\frac{7 \sqrt{1-x^{3}}}{6} \] \[ y^{\prime}= \]2 answers -
9. Find \( f_{x y} \) if \( f(x, y)=\frac{4 x^{2}}{y}+\frac{y^{2}}{2 x} \) (a) \( -\frac{8 x}{y^{2}}-\frac{y}{x^{2}} \) (b) \( 8 x-y \) (c) \( 8 x+y \) (d) \( \frac{16 x^{3} y-8 x^{4}+2 x y^{3}-y^{4}}2 answers -
Solve b
Evalúe \( \int_{c} F \cdot d r \) donde \( C \) está representada por \( r(t) \). a) \( F(x, y)=3 x i+4 y j ; C: r(t)=\cos (t) i+\operatorname{sen}(t) j \) donde \( 0 \leq t \leq \pi / 2 \) b) \( F(2 answers -
Encuentre la transformada de Laplace de f (t) = {{ 0 ≤t≤1 t> 1
Encuentre la transformada de Laplace de \[ f(t)=\left\{\begin{array}{lr} t, & 0 \leq t \leq 1 \\ 1, & t \geq 1 \end{array}\right. \]2 answers -
Usando la definición de la derivada \( f^{\prime}(x)=\lim _{h \rightarrow 0} \frac{f(x+h)-f(x)}{h} \) Determine la derivada de \( f(x)=2 x^{3}-5 x^{2}+3 x-4 \)2 answers -
2) (10 puntos) Determine el volumen de revolución de \( y=x^{3} \), bordeado por el eje de \( x \) y \( x=0 \) y \( x=2 \), rotando alrededor del eje de \( x \).2 answers -
Para la siguiente función, complete los espacios en blanco de la tabla, al usar los criterios de la primera y segunda derivadas. Finalmente, use la herramienta Desmos para ilustrar la gráfica de la2 answers -
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Mostrar trabajo Solución: y=C 1 e -x cosx+C 2 e -x senx Ecuación diferencial:y (2) + 2y (1) + 2y = 02 answers
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