Calculus Archive: Questions from February 18, 2023
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2 answers
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Do all 4 parts
1. Compute the derivative of the following functions. a. \( y=\sqrt{e^{5 x}+3 x^{4}} \) b. \( y=2^{\sin (3 x)} \) c. \( y=\ln \left(\cos ^{-1}\left(x^{3}\right)\right) \) d. \( y=\log \left(x^{2} \sqr2 answers -
2 answers
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Help
\[ F(x, y, z)=x^{3}+4 x^{2} y-2 y-z \] hat is \( \nabla F(P) \) when \( P=(-1,2,1) \) a. \( (-13,-2,-2) \) b. \( (13,2,-1) \) C. \( (-12,2 y-1) \) d. \( (-13,2,-1) \)2 answers -
2 answers
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\( \lim _{x \rightarrow \infty} \frac{7 x^{3}+2 x-5}{4-2 x+5 x^{2}-3 x^{3}}[\mathrm{~K} / \mathrm{U} 2 \) marks]2 answers -
Answer whether True or False
\( f(x, y)=x^{3}+4 x^{2} y-2 y, \nabla f(x, y)=\left(3 x^{2}+8 x y, 4 x^{2}-2\right) \)2 answers -
2 answers
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Compute the gradient vector fields of the following functions: A. \( f(x, y)=3 x^{2}+10 y^{2} \) \( \nabla f(x, y)= \) B. \( f(x, y)=x^{6} y^{10} \), \( \nabla f(x, y)=\quad \mathbf{i}+\quad \mathbf{j2 answers -
Can you give me the answers
I. [11 Ptos] Cierto o Falso. 1. Si \( f(x) \) no tiene puntos removibles ni brincos en \( x=a \), entonces \( \lim _{x \rightarrow} f(x)=f(a) \). 2. Si \( f(x) \) es continua en \( x=a \), entonces \(2 answers -
please answer both questions 2 and 3
2. Encuentre un vector unitario en la dirección de \( \vec{v}=2 i+j+2 k \) a. \( \vec{u}=\frac{2}{\sqrt{5}} i+\frac{1}{\sqrt{5}} j+\frac{1}{\sqrt{5}} k \) b. \( \vec{u}=\frac{2}{9} i+\frac{1}{9} j+\f2 answers -
4. Dada la ecuación \( \frac{x^{2}}{4}+\frac{y^{2}}{9}+\frac{z^{2}}{36}=1 \) a. Identifique la gráfica b. Complete la siguiente tabla: c. Grafique la ecuación2 answers -
2 answers
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2 answers
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Find h(x, y) = g(f(x, y)).g(t) = t + ln(t), f(x, y) = 4 − xy 4 + x2y2
Find \( h(x, y)=g(f(x, y)) \) \[ g(t)=t+\ln (t), \quad f(x, y)=\frac{4-x y}{4+x^{2} y^{2}} \] \[ h(x, y)= \]3 answers -
2 answers
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(1 point) Find \( y \) as a function of \( t \) if \[ 36 y^{\prime \prime}+156 y^{\prime}+169 y=0 \] \( y(0)=8, \quad y^{\prime}(0)=8 \). \( y= \)2 answers -
La suma de infinito negativo cuatro veces es; a. negativo infinito b. positivo infinito c. \( 4-\infty \) d. \( 4 \infty \)2 answers -
Hallar el numero donde la \( f(x)=\left\{\begin{array}{l}\frac{x^{2}-25}{x+5}, \text { si } x \neq 2 \\ -3, \text { si } x=2\end{array}\right. \) es continua. a. Es continúa en el punto \( -5 \) b. E2 answers -
Calcula el limite de la siguiente funcion cuando \( x \) se acerca a negativo infinito; \[ f(x)=\sqrt{2 x^{4}-5 x^{3}+2} \] a. \( -\infty \) b. \( -2 \infty \) c. \( \infty \) d. \( 2 \infty \)2 answers -
Cuando \( x \rightarrow-\infty \) de la \( f(x)=\frac{2 x^{2}+4 x-7}{2 x-4} \) el Limite es; a. 1 b. \( -2 \) c. 2 d. \( -1 \)2 answers -
2 answers
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Evaluate the integral. \[ \int \frac{\sqrt{y^{2}-121}}{y} d y, y>11 \] \[ \int \frac{\sqrt{y^{2}-121}}{y} d y= \]2 answers -
Solve the following initial value problems: \( \frac{d y}{d t}=6 t \) A. \( y(0)=8: \quad y= \) B. \( y(0)=4: \quad y= \)2 answers -
26. The domain of the function \( f(x, y)=3 x+5 y+2 \) is (A) \( \left\{(x, y) \in \mathbb{R}^{2}: x, y \geq 0\right\} \) (B) \( \left\{(x, y) \in \mathbb{R}^{2}: y2 answers