Calculus Archive: Questions from September 10, 2023
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Find \( f_{x} \) and \( f_{y} \) if (a) \( f(x, y)=\sqrt{y-x} \ln (y+x) \). (b) \( f(x, y)=\log _{y} x \).1 answer -
A boat leaves the port with a heading of N35°E. Just 70 miles north of the pier is Pichones Island. How far (in miles) has he traveled when the boat is just east of the island? (at the same latitude)
Un bote sale del puerto con un rumbo de \( \mathrm{N} 35^{\circ} \mathrm{E} \). Justo a 70 millas al Norte del muelle se encuentra la isla Pichones. ¿Cuánta distancia (en millas) ha recorrido cuando1 answer -
Find the general solution of the following Lagrange linear equations: 1. (i) \( p+q=\sin x \) (ii) \( a p+b q=c \) (iii) \( p \tan x+q \tan y=\tan z \) (iv) \( y z p+z x q=x y \) (v) \( x p+y q=z \) (1 answer -
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I. Considere la función \( w=\operatorname{sen}(2 x+3 y) \) donde \( x=s+t \) y \( y=s-t \quad \) para determinar a) \( \frac{\partial w}{\partial s} \quad \) para \( s=0 \quad y \quad t=\frac{\pi}{21 answer -
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Please show Explanations and Justifications on procedures. Use (a) the cylindrical shells method and (b) the washer method to find the volume of the donut created when the circle x2+y2=4 is rotated ar
4. Usa (a) el método de capas cilíndricas (cylindrical shells) y (b) el método de arandelas, para encontrar el volumen de la "dona" creada cuando el círculo \( x^{2}+y^{2}=4 \) se rota alrededor d0 answers -
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If \( 4 x-13 \leq g(x) \leq x^{2}-6 x+12 \) for all \( x \geq 0 \), find \( \lim _{x \rightarrow 5} g(x) \)1 answer -
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1. For the following exercises, find \( \frac{d y}{d x} \) for the given functions a. \( y=5 \csc x+\frac{2}{x^{2}} \) b. \( y=x-x^{3} \sin x \) c. \( y=\sin x \cos x \) d. \( y=\frac{\tan x}{1-\sec x1 answer -
Find the \( \frac{d^{2} x}{d x^{2}} \) for the given functions. a. \( y=\frac{1}{x}+\tan x \) b. \( y=3 \sin x+x^{2} \cos x \) c. \( y=\sec x+\cot x \)1 answer -
For the function y = f(x) = x² - 4x − 4, x ≥ 2, find (ƒ-¹)'(11) = df-1 dy ly-11
For the function \( y=f(x)=x^{2}-4 x-4, x \geq 2 \), find \( \left.\frac{d f^{-1}}{d y}\right|_{y=11} \) \( \left(f^{-1}\right)^{\prime}(11)= \)1 answer -
Find dy/dx at the value of the parameter. x = 3 cos(2𝜋s), y = 2 sin(2𝜋s), s = − 1/4
Find \( \frac{d y}{d x} \) at the value of the parameter. \[ x=3 \cos (2 \pi s), y=2 \sin (2 \pi s), s=-\frac{1}{4} \]1 answer -
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Word y su editor de ecuaciones para realizar la actividad. Tiene dos (2) intentos para completar la actividad satisfactoriamente. Esta actividad tiene un valor de 20 puntos. Para enviar a actividad de1 answer -
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z = √25-x² - y² C. Z= (x, y) varia de (1,1) a (1.01,0.97)
c. \( z=\sqrt{25-x^{2}-y^{2}} \quad(x, y) \) varia de \( (1,1) a(1.01,0.97) \)1 answer -
22) \( \lim _{y \rightarrow 4} \frac{\frac{1}{y+1}-\frac{1}{5}}{y-4}= \) 23) \( \lim _{x \rightarrow 0} \frac{\sqrt{5 x+25}-5}{x}= \)1 answer -
find the center of mass of a planar lamina for the following.
15. \( y=\frac{1}{2} x, y=0, x=2 \) 16. \( y=6-x, y=0, x=0 \) 17. \( y=\sqrt{x}, y=0, x=4 \) 18. \( y=\frac{1}{3} x^{2}, y=0, x=2 \) 19. \( y=x^{2}, y=x^{3} \) 20. \( y=\sqrt{x}, y=\frac{1}{2} x \) 211 answer -
#23, find arc length
19. \( y=\sin x, \quad 0 \leq x \leq \pi \) 20. \( y=\cos x, \quad-\frac{\pi}{2} \leq x \leq \frac{\pi}{2} \) 21. \( x=e^{-y}, \quad 0 \leq y \leq 2 \) 22. \( y=\ln x, \quad 1 \leq x \leq 5 \) 23. \(1 answer -
Find a possible equation for a linear function with the given contour diagram. \( h(x, y)=4+2 x-y \) \( h(x, y)=2+x-2 y \) \( h(x, y)=4+x-y \) \( h(x, y)=4+x+y \) \( h(x, y)=-4+2 x- \)1 answer -
2. (3 pts) If \( 4 x-13 \leq g(x) \leq x^{2}-6 x+12 \) for all \( x \geq 0 \), find \( \lim _{x \rightarrow 5} g(x) \).1 answer -
Calculate the volume using the slice method for the pyramid with a height of 5 Units, and with an isosceles triangle as the base with sides of lengths of 6 units and 8 units, as shown in the figure.
1. Calcula el volumen usando el método de rebanadas para la pirámide con altura de 5 unidades, y con un triángulo isósceles como base con lados de longitudes de 6 unidades y 8 unidades, como se mu1 answer -
If y= 7x + 8/x^4, find dy/dx at x=1.
\( y=7 x+\frac{8}{x^{4}} \), find \( \frac{d y}{d x} \) at \( x=1 \)1 answer -
2. Rotate the ellipse x^2/a^2 + y^2/b^2 = 1 around the x-axis to generate the volume of a "American football" ball, as shown in the figure. Calculate the volume generated using (a) the cut method and
2. Rota la elipse \( x^{2} / a^{2}+y^{2} / b^{2}=1 \) alrededor del eje \( x \) para generar el volumen de una pelota de "football" americano, como se muestra en la figura. Calcula el volumen generado1 answer -
What is the volume of the "biscuit" that results from rotating the region between y = 0, Y = 4/pi^2 x(pi-x) from x = 0 to x = pi, around the y axis?
3. ¿Cuál es el volumen del "bizcocho" que resulta de rotar la región entre \( y=0 \), \( y=\frac{4}{\pi^{2}} x(\pi-x) \) desde \( x=0 \) a \( x=\pi \), alrededor del eje \( y ? \)1 answer -
Find the surface area of the volume generated when the curve y = x^2 rotates around the axis and from (1,1) to (3,9).
5. Encuentra el área de la superficie del volumen generado cuando la curva \( y=x^{2} \) gira alrededor del eje y desde \( (1,1) \) hasta \( (3,9) \).1 answer -
c) \( \lim _{x \rightarrow 2} \frac{\sqrt{x-2}}{x-2} \) f) \( \lim _{x \rightarrow \infty} \frac{3 x^{3}-x^{2}}{5 x^{2}+5 x} \)1 answer -
help please!
Determine the function, \( y \), given: a. \( y^{\prime}=\frac{2}{x}-4 \sqrt{x} \) b. \( y^{\prime \prime}=\frac{3}{2} x+x^{3} \)1 answer