Calculus Archive: Questions from February 14, 2023
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Take the derivative. (a) \( y=(\sqrt{x}+1)^{100} \) (b) \( J(\theta)=\tan ^{2}(3 \theta) \) (c) \( f(x)=\sin (\cos (\sqrt{x+1})) \) (d) \( y=\sqrt{x+\sqrt{x+\sqrt{x}}} \)2 answers -
Please answer 14,16,18,22 without using the chain rule. Thank you
1-22 Differentiate. 1. \( f(x)=3 \sin x-2 \cos x \) 2. \( f(x)=\tan x-4 \sin x \) 13. \( f(\theta)=\frac{\sin \theta}{1+\cos \theta} \) 14. \( y=\frac{\cos x}{1-\sin x} \) 3. \( y=x^{2}+\cot x \) 4. \2 answers -
2 answers
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2 answers
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Find \( \lim _{x \rightarrow 0} f(x) \) if, for all \( x, 8 \cos (3 x) \leq f(x) \leq 7 x^{2}+8 \) \[ \lim _{x \rightarrow 0} f(x)= \]2 answers -
0 answers
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Represent the plane \( 15 x-y-5 z=20 \) as the graph of a two-variable function, \( f(x, y) \), and as the level surface of a threevariable function, \( g(x, y, z)=c \). \[ \begin{array}{l} z=f(x, y)=2 answers -
find the derivative using quotient rules?
1. \( y=x^{3} \csc x \) 2.. \( y=3 t^{2} \tan t \) 3. \( y=\frac{\sin x}{1-\cos x} \) 4. \( y=\frac{1+\sqrt{t}}{1-\sqrt{t}} \) 5. \( y=\frac{1}{t^{4}+2} \) \( 6 \quad y=\frac{e^{x}}{x^{2}} \)2 answers -
20 If \( z=e^{x} \sin y, x=\sin t, y=\cos t \). then at \( t=0, \frac{d z}{d t}=1 \) \begin{tabular}{|l|l} \hline \( \mathbf{A} \) & True \\ \hline \end{tabular} \begin{tabular}{|l|l} B & False \\ \hl2 answers -
I posted in English and Spanish.
Calcular la forma compleja de la serie de Fourier, deducir la forma trigonómetrica de la serie de Fourier y dibujar los espectros de frecuencia para la función \( f(t) \) definida por \[ f(t)=-\frac2 answers -
This is Complex Numbers. I posted in English and Spanish.
Determine la solución de la ecuación de onda utilizando la transformada de Fourier y dando la respuesta en términos de la transformada inversa de Fourier. \[ \begin{array}{c} \frac{\partial^{2} u}{0 answers -
2 answers
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2 answers
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Determine \( h^{\prime}(x) \) when \( h(x)=0.02 e^{x} x^{3} \) Select the correct answer below: \[ \begin{array}{l} h^{\prime}(x)=0.02\left(e^{x}\right)\left(3 x^{2}\right) \\ h^{\prime}(x)=0.02\left(2 answers -
For the function \( y=f(x)=x^{2}+3 x+2, x \geq-1.5 \), find \( \left.\frac{d f^{-1}}{d y}\right|_{y=11} \) \[ \left(f^{-1}\right)^{\prime}(11)= \]2 answers -
help here plzzzz
Evalúe cada una de las siguientes integrales. 6. \[ \int \frac{d x}{\sqrt{e^{x}-1}} \] 7. \[ \int \frac{\operatorname{sen}(\ln t)}{t} d t \] 8. \[ \int e^{x} \cos x d x \] 9. \[ \int \frac{d t}{2 t^{2 answers -
help right here plz
Calcule y' en cada una de las siguientes funciones. 1. \[ y=\frac{\tan x}{1+\cos x} \] 2. \[ y=x \cos ^{-1} x \] 3. \[ x e^{y}=y \operatorname{sen} x \] 4. \[ y=\sqrt{x} \cos \sqrt{x} \] 5. \[ x e^{y}2 answers -
Find \( d y / d x \) by implicit differentiation. \[ \tan (x-y)=\frac{y}{3+x^{2}} \] \[ y^{\prime}= \]2 answers -
\( \begin{array}{l}\quad z=\arcsin (x-y), \quad x=s^{2}+t^{2}, \quad y=4-8 s t \\ \frac{\partial z}{\partial s}= \\ \frac{\partial z}{\partial t}=\end{array} \)2 answers -
Find \( y^{\prime} \) and \( y^{\prime \prime} \). \[ y=\ln (6+\ln (x)) \] \[ y^{\prime}= \] \[ y^{\prime \prime}= \] 4. [-/1 Points \( ] \) SCALCET8 Find the derivative of the function. \[ G(x)=\sqrt2 answers -
2 answers
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2 answers
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2 answers
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Let \( \sqrt{y}-\sqrt{x}=1 \). Find \( y^{\prime} \). Choose the correct answer from the following below. \[ \begin{array}{l} y^{\prime}=\sqrt{x} \\ y^{\prime}=\sqrt{x}-2 \sqrt{y} \\ y^{\prime}=-2 \sq2 answers -
(1 point) Let \( f(x, y, z)=\frac{x^{2}-5 y^{2}}{y^{2}+6 z^{2}} \). Then \[ \begin{array}{l} f_{x}(x, y, z)= \\ f_{y}(x, y, z)= \\ f_{z}(x, y, z)= \end{array} \]2 answers -
please an equation for each of y=____
\( y= \) \( y= \) Graph C Graph D \( y= \) \( y= \) Graph E Graph F \( y= \) \( y= \)0 answers -
Integrate. \[ \int\left(7 \mathrm{x}^{4}+\frac{2}{\mathrm{x}^{6}}-e^{7 \mathrm{x}}\right) \mathrm{dx}=\quad+\mathrm{C} \]2 answers