Calculus Archive: Questions from December 06, 2023
-
5. Differentiate the following functions \[ y=\ln |\sec x|, \quad y=\sqrt{\frac{x-1}{x^{4}+1}}, \quad y=(\cos x)^{x}, \quad y=\frac{e^{-x} \cos ^{2} x}{x^{2}+x+1} \]1 answer -
Q(1) If \( y^{\prime \prime}+36 y=0, y(0)=0, y^{\prime}(0)=6 \), then \( y(\pi)= \) a) -1 b) 1 c) \( \frac{1}{2} \) d) 0 Q(2) If \( y_{1}=x \) is a solution \( f \)1 answer -
Solve the given differential equation. \[ \begin{aligned} 9 y^{\prime \prime}+ & 30 y^{\prime}+25 y=0 \\ y & =\left(c_{1}+c_{2} x\right) e^{-5 x / 3} \\ y & =c_{1} e^{-5 x / 3}+c_{2} \\ y & =c e^{-5 x1 answer -
Solve the given differential equation. \[ \begin{array}{c} 9 y^{\prime \prime}+30 y^{\prime}+25 y=0 \\ y=\left(c_{1}+c_{2} x\right) e^{-5 x / 3} \\ y=c_{1} e^{-5 x / 3}+c_{2} \\ y=c e^{-5 x / 3} \\ y=1 answer -
Find the Jacobian \( \frac{\partial(x, y, z)}{\partial(u, v, w)} \), where \( x=3 u+v, y=u-2 w, z=v+w \)1 answer -
\( \begin{array}{c}F(x)=\int_{6}^{e^{x}}\left(y^{2} \sin (y)\right) d y \\ F^{\prime}(x)=\end{array} \)1 answer -
7.1 4
Find the values of the function. \[ f(x, y)=e^{x y} \] (a) \( f(x+h, y)-f(x, y) \) (b) \( \quad f(x, y+h)-f(x, y) \)1 answer -
1 answer
-
1 answer
-
0 answers
-
1 answer
-
Given \( f(x, y)=-4 x^{4}+6 x y^{5}-5 y^{3} \) \[ \begin{array}{l} f_{x x}(x, y)= \\ f_{x y}(x, y)= \end{array} \] Question Help:1 answer -
Encuentre el límite, si existe, o demuestre que el límite no existe.
i) \( \lim _{(x, y) \rightarrow(5,-2)}\left(x^{5}+4 x^{3} y-5 x y^{2}\right) \)1 answer -
0 answers
-
0 answers
-
0 answers
-
0 answers
-
1 answer
-
1 answer
-
0 answers
-
1 answer
-
1 answer
-
1 answer
-
1 answer
-
1 answer
-
If \( z=f(x, y) \), where \( f \) is differentiable, and \[ \begin{array}{rlrl} x & =g(t) & y & =h(t) \\ g(5) & =-6 & h(5) & =9 \\ g^{\prime}(5) & =3 & h^{\prime}(5) & =1 \\ f_{x}(-6,9) & =-4 & f_{y}(1 answer -
1 answer
-
0 answers
-
1 answer
-
(1 point) Find \( y \) as a function of \( x \) if \[ y^{\prime \prime \prime}-11 y^{\prime \prime}+24 y^{\prime}=70 e^{x} \] \[ \begin{array}{l} y(0)=16 \quad \cdot /(n)=26 . \quad v^{\prime \prime}(1 answer -
A. \( \operatorname{Si} 3^{x+1}=6 \) entonces \( x= \) B. El \( \log _{2} 16+\log _{3}(9) \) es igual a : C. Suponga que \( \mathrm{C}(x) \) representa el costo total en dólares en la producción de1 answer -
2. [3 pts cada uno] Llena los blancos a) \( \operatorname{Si} f(x)=\frac{4}{x^{2}}-4^{x}+\log _{4} x \) entonces \( f^{\prime}(x)= \) b) \( \operatorname{Si} f(x)=e^{2 x+3} \) entonces \( f^{\prime \p1 answer -
1 answer
-
1 answer
-
1 answer
-
1 answer
-
1 answer
-
1 answer
-
1 answer
-
1 answer
-
1 answer
-
6.) \( \int x \sec ^{2}\left(x^{2}\right) d x= \) 7.) \( \int \frac{e^{x}-e^{3 x}}{e^{2 x}} d x= \) 8.) \( \int \sec ^{2} x \tan x d x= \) 9.) \( \int \frac{1}{(x+5)^{3}} d x \) 12.) \( \int \cos x(31 answer -
1 answer
-
1 answer
-
\( \begin{array}{l}\text { Find } \frac{d^{2} y}{d x^{2}} \\ 12 x^{2}+y^{2}=3 \\ \frac{d^{2} y}{d x^{2}}=\end{array} \)1 answer -
0 answers
-
0 answers
-
solve 9-11
6.) \( \int x \sec ^{2}\left(x^{2}\right) d x= \) 9.) \( \int \frac{1}{(x+5)^{3}} d x \) 7.) \( \int \frac{e^{x}-e^{3 x}}{e^{2 x}} d x= \) 10.) \( \int \sec x \tan x(\sec x-1) d x= \) 8.) \( \int \sec1 answer -
0 answers
-
0 answers
-
1 answer
-
Let \( z=\frac{\csc y}{y^{4}} \) Choose the correct form for the derivative and fill in the values of the letters \( A, B, C, D \). \[ \begin{aligned} \frac{d z}{d y} & =\frac{A y^{B} \csc y \cot y+C1 answer -
need help plzz asap
\( \sin ^{3} \theta+\sin \theta \cos ^{2} \theta=\sin \theta \) \( \cot ^{2} \theta-\cos ^{2} \theta=\cos ^{2} \theta \cot ^{2} \theta \) \( \cos ^{3} x \sin ^{2} x=\left(\sin ^{2} x-\sin ^{4} x\right1 answer -
Find \( \operatorname{curl}(\mathbf{F} \times \mathbf{G}) \) \[ \begin{array}{l} \mathbf{F}(x, y, z)=8 \mathbf{i}+9 x \mathbf{j}+10 y \mathbf{k} \\ \mathbf{G}(x, y, z)=8 x \mathbf{i}-8 y \mathbf{j}+81 answer -
1 answer
-
Given f(x, y) = −x¹ — 4xy³ – 2y³, find faz(x, y) = fry(x, y) = Question Help: Video
Given \( f(x, y)=-x^{4}-4 x y^{3}-2 y^{5} \), \[ \begin{array}{l} f_{x x}(x, y)= \\ f_{x y}(x, y)= \end{array} \] Question Help: Video1 answer -
1 answer
-
[ E = {(x, y, z) | −5 ≤ y ≤ 0,0 ≤ x ≤ y, 0 < z
Evaluate \( \iiint_{E}(x+y-3 z) d V \) where \[ \begin{array}{l} E=\left\{(x, y, z) \mid-5 \leq y \leq 0,0 \leq x \leq y, 01 answer -
Find the gradient vector field \( (\vec{F}(x, y, z)) \) of \( f(x, y, z)=\sqrt{5 x^{2}+y^{2}+6 z^{2}} \). \[ \vec{F}(x, y, z)= \]1 answer -
1 answer
-
1 answer
-
Apply Green's Theorem to evaluate the integral. \( \oint_{C}(y+x) d x+(y+6 x) d y \) C: The circle \( (x-6)^{2}+(y-3)^{2}=7 \)1 answer -
1 answer
-
1 answer
-
2. Evaluate the following derivatives: a) \( y=x \cot ^{-1}(x / 3) \) b) \( y=\tan ^{-1}\left(e^{4 x}\right) \) c) \( y=\sin ^{-1}\left(\frac{1}{x}\right) \)1 answer -
0 answers
-
Establish a triple integral for the volume of the pyramid enclosed by the planes NOTE: Just set up the integral with correct limits and differentials Do not evaluate .
2. Establecer, pero no evaluar, una integral triple para el volumen de la pirámide encerrada por 1 planos \[ \frac{x}{B}+\frac{y}{C}+\frac{z}{D}=1, \quad x=0, \quad y=0, \quad z=0 \] Nota: Los vérti1 answer -
Calculate the gradient field of the function Step by step
3. Calcular el campo gradiente de la función \[ f(x, y, z)=\frac{A x}{C y+E z} \] 3) calculate the gradient field of the function \[ f(x, y, z)=\frac{4 x}{5 y+3 z} \]1 answer -
Calculate the divergence of this vectorial field Calcular la divergencia de este campo vectorial
4. Calcular la divergencia de este campo vectorial. \[ \overrightarrow{\mathbf{F}}(x, y, z)=\left(\frac{B x}{x^{2}+y^{2}+z^{2}}\right) \hat{\mathbf{i}}+\left(\frac{D y}{x^{2}+y^{2}+z^{2}}\right) \hat{1 answer -
1 answer
-
1 answer
-
1 answer
-
1 answer
-
Find all the second partial derivatives. \[ \begin{array}{l} f(x, y)=x^{6} y^{9}+6 x^{5} y \\ f_{x x}(x, y)= \\ f_{x y}(x, y)= \\ f_{y x}(x, y)= \\ f_{y y}(x, y)= \end{array} \]1 answer -
1 answer
-
1 answer
-
1 answer
-
1 answer
-
0 answers
-
1 answer
-
1 answer
-
#1 and 14 please
1-54 Use the guidelines of this section to sketch the curve. 1. \( y=x^{3}+3 x^{2} \) 2. \( y=2 x^{3}-12 x^{2}+18 x \) 3. \( y=x^{4}-4 x \) 4. \( y=x^{4}-8 x^{2}+8 \) 5. \( y=x(x-4)^{3} \) 6. \( y=x^{1 answer -
#10, 12 and 14
In Problems 1 through 20, find a particular solution \( y_{p} \) of the given equation. In all these problems, primes denote derivatives with respect to \( x \). 1. \( y^{\prime \prime}+16 y=e^{3 x} \1 answer -
Differentiate: \[ \begin{array}{l} f(x)=\left(x^{4}+8 x\right) e^{x} \\ \left(x^{4}+8 x+3 x^{4}+8\right) x \\ \left(7 x^{4}+8 x\right) e^{x} \\ e^{x}\left(x^{4}+8 x+3 x^{4}+8\right) \\ e^{x}\left(x^{41 answer -
1 answer
-
1 answer
-
1 answer
-
30. Considerando una aplicación de las derivadas parciales para estimar valores, utilice esto para estimar la cantidad de metal en una lata cilíndrica cerrada que mide \( 10 \mathrm{~cm} \) de altur1 answer -
22. Si consideramos \( g(x, y, z)=\sqrt{1+x z}+\sqrt{1-x y} \) encuentre \( g_{x y z} \). [Hint. Utilizar el hecho que es una suma de funciones \( \mathrm{y} \) derivar parcialmente en un orden difere1 answer -
19. Dada \( g(x, y)=\left(x^{2}+1, y^{2}\right) \) y \( f(u, v)=\left(u+v, u, v^{2}\right) \), calcular la derivada de \( f \circ g \) en \( (1,1) \) usando la regla de la cadena.1 answer -
Trace cada una de las regiones encerradas y su área. 1. \( y=12-x^{2}, y=x^{2}-6 \) 2. \( y=\cos x, y=2-\cos x, 0 \leq x \leq 2 \pi \) 3. \( x=2 y^{2}, x=4+y^{2} \)1 answer -
Derivada implícita 28. Considerando la derivación implícita determinar \( \frac{\partial z}{\partial x}, \frac{\partial z}{\partial y} \). i) \( x^{2}+2 y^{2}+3 z^{2}=1 \) ii) \( x^{2}-y^{2}+z^{2}-1 answer -
27. Considerando el teorema de igualdad de derivadas mixtas (conocido como Teorema de Clairaut) considera que las funciones son de clase \( \mathrm{C}^{2} \) entonces utilice este hecho para demostrar1 answer -
24. Si consideramos la siguiente expresión \( w=e^{b_{1} x_{1}+b_{2} x_{2}+\cdots+b_{n} x_{n}} \), donde \( b_{1}{ }^{2}+{b_{2}}^{2}+\cdots+b_{n}{ }^{2}=1 \), muestre que: \[ \frac{\partial^{2} w}{\p1 answer -
0 answers
-
1 answer
-
1 answer
-
6. a) Demuestre que una función derivable \( f \) disminuye de manera más rápida en \( x \) en la dirección opuesta al vector gradiente, es decir, en la dirección de \( -\vec{\nabla} f \) y que l1 answer -
\[ T(x, y, z)=200 e^{-x^{2}-3 y^{2}-9 z^{2}} \] Donde \( \mathrm{T} \) se mide en grados Celsius y \( x, y, z \) en metros. a) Determine la razón de cambio de temperatura en el punto \( \mathrm{P}(2,1 answer -
1 answer