Calculus Archive: Questions from March 06, 2023
-
2 answers
-
2 answers
-
2 answers
-
Find the exact value without a calculator. 21. \( \cos \left(\sin ^{-1}\left(\frac{1}{2}\right)\right) \) 22. \( \sin \left(\cos ^{-1}\left(\frac{\sqrt{2}}{2}\right)\right) \) 23. \( \sin ^{-1}\left(\2 answers -
2 answers
-
2 answers
-
Find the limit. \[ \lim _{(x, y) \rightarrow(0,0)}^{x \neq y} \frac{5 \sqrt{y}-5 \sqrt{x}+\sqrt{x y}-x}{\sqrt{y}-\sqrt{x}} \] 0 10 5 No limit2 answers -
27. \( \int \sqrt{\left(2 x-x^{2}\right)} d x \) 28. \( \int \frac{4 x-2}{x^{3}-x} d x \) 29. \( \int \frac{x^{4}}{x^{2}-2} d x \) 30. \( \int \frac{\sec x \tan x}{\sec x+\sec ^{2} x} d x \) 31. \( \i2 answers -
1.Consideremos la función z = f (x, y) = ln( xy) + y2 y a las variables x , y definidas por x = e^2t , y = e^2t . a) Haga un diagrama de variables b) ¿Finalmente de cuántas variables depende la var
1. Consideremos la función \( z=f(x, y)=\ln (x y)+y^{2} \) y a las variables \( x, y \) definidas por \( x=e^{2 t}, y=e^{-2 t} \) a) Haga un diagrama de variables b) ¿Finalmente de cuántas variable2 answers -
2 answers
-
3 answers
-
2 answers
-
Considere la siguiente gráfica para hallar los limites en de su función según solicitado. 1) \( \lim _{x \rightarrow-2^{-}} f(x)= \) 2) \( \lim _{x \rightarrow-2^{+}} f(x)= \) 3) \( \lim _{x \right2 answers -
Find \( \iint_{R} f(x, y) d A \) where \( f(x, y)=1 x+4 \) and \( R=[2,4] \times[-3,-2] \). \[ \iint_{R} f(x, y) d A= \]2 answers -
2. Find \( d y / d x \). (a) \( y=\frac{4}{3 \pi} \sin (3 x)+\frac{4}{5 \pi} \cos (5 x) \) (c) \( y=(4 x+3)^{4}(x+1)^{-1} \) (b) \( y=\frac{1}{18}(3 x-2)^{6}+\left(4-\frac{1}{2 x^{2}}\right)^{-1} \) (2 answers -
Find the derivative of the function. Simplify if possible. \[ y=\arccos \left(e^{9 x}\right) \] \[ y^{\prime}= \]2 answers -
Find derivative, show all steps
\[ \text { 7) } y=\ln \left[(5 x-7)^{4}(2 x+3)^{3}\right] \] 8) \( y=\left(\frac{x^{2}-1}{2 x^{3}+1}\right)^{4} \)0 answers -
Evaluate the double integral \[ \iint_{D} 3 e^{y^{2}} d A \] where \( D=\{(x, y) \mid 0 \leq x \leq 4 y, 0 \leq y \leq 2\} \)2 answers -
Question #8
Evaluate the integral. 8) \( \int 5 \cos ^{4} 3 x d x \) A) \( \frac{15}{8} x+\frac{5}{6} \sin 6 x+\frac{5}{32} \sin 12 x+C \) B) \( \frac{15}{4} x+\frac{5}{12} \sin 3 x+\frac{5}{96} \sin 6 x+C \) C)2 answers -
Question #10
raluate the integral. 8) \( \int 5 \cos ^{4} 3 x d x \) A) \( \frac{15}{8} x+\frac{5}{6} \sin 6 x+\frac{5}{32} \sin 12 x+C \) B) \( \frac{15}{4} x+\frac{5}{12} \sin 3 x+\frac{5}{96} \sin 6 x+c \) C) \2 answers -
2 answers
-
17
In Exercises 9-20, use the Chain Rule to calculate \( \frac{d}{d t} f(r(t)) \) at the value of \( t \) given. 7. \( f(x, y)=\ln x+\ln y, \quad \mathbf{r}(t)=\left\langle\cos t, t^{2}\right\rangle, \q2 answers -
solve f and h please
2. For each function, determine \( \frac{d y}{d x} \). a) \( y=x \) b) \( y=\frac{1}{4} x^{2} \) c) \( y=x^{5} \) d) \( y=-3 x^{4} \) e) \( y=1.5 x^{3} \) f) \( y=\sqrt[5]{x^{3}} \) g) \( y=\frac{5}{x2 answers -
2 answers
-
2 answers
-
Calcule la derivada direccional de la función en el punto dado en la dirección del vector v. 2 answers
-
2 answers
-
(1 point) Let \( f(x, y, z)=\frac{x^{2}-2 y^{2}}{y^{2}+5 z^{2}} \). Then \[ \begin{array}{l} f_{x}(x, y, z) \\ f_{y}(x, y, z)= \\ f_{z}(x, y, z)= \end{array} \]2 answers -
2 answers
-
Determine \( f_{x} \) and \( f_{y} \) if (A) \( f(x, y)=(\sin (\sqrt{x})) \ln \left(y^{2}\right) \) \( f_{x}= \) \( f_{y}= \) (B) \( f(x, y)=\sin \left(\sqrt{x} \ln \left(y^{2}\right)\right) \)2 answers -
For \( f(x, y) \), find all values of \( x \) and \( y \) such that \( f_{x}(x, y)=0 \) and \( f_{y}(x, y)=0 \) simultaneously. \[ \left.\begin{array}{l} \quad f(x, y)=\ln \left(2 x^{2}+5 y^{2}+2\righ2 answers -
Please help!
Find \( \int_{0}^{2} f(x, y) d x \) and \( \int_{0}^{3} f(x, y) d y \) \[ f(x, y)=5 y \sqrt{x+2} \] \[ \int_{0}^{2} f(x, y) d x= \]2 answers -
2. Find the linear approximation of \( f(x, y) \) at the given point. (a) \( f(x, y)=1+x \ln (x y-5) \), (2,3) (b) \( f(x, y)=e^{-x y} \cos y,(\pi, 0) \) (c) \( f(x, y)=\sqrt{x+e^{4 y}},(3,0) \)2 answers -
3. Differentiate to find \( y^{\prime} \). Simplify your answers. a. \( y=\csc \left(t^{2}+t\right) \) b. \( y=\sin ^{4}(2 \theta) \) c. \( y=\frac{e^{2 t}}{1+e^{2 t}} \) d. \( y=x\left(x^{2}+1\right)2 answers -
Solve the differentiable equations
RESUELVA LAS SIGUIENTES ECUACIONES DIFERENCIALES \[ \frac{d y}{d x}=10-y \] \( \frac{d y}{d x}=\frac{x-y}{x} \)2 answers -
Check that y = xsen(x) + xcos(x) it is a solution of the differential equation y" + y = 2cos(x) - 2
6. Compruebe que \( y=x \operatorname{sen}(x)+x \cos (x) \) es una solución de la ecuación diferencial \[ y^{\prime \prime}+y=2 \cos (x)-2 \]2 answers -
El porcentaje, y, de hogares que poseen Lavaplatos \( t \) años después han sido introducidos en un país está modelado por \( f(t)=33-17 e^{-0.2 t} \) Encuentre el porcentaje de hogares con lavapl2 answers -
La gráfica de \( y=f(x) \) se muestra a continuación. Usar la gráfica para contestar la progunta. ¿Es \( f(x) \) continua en \( x=-1 \) ? Select one: A. \( \mathrm{Si} \) B. No Usar la gráfica p2 answers -
LARAPCALC10 2.2.052. Find \( f^{\prime}(x) \). \[ f(x)=8 x^{2}-5 x^{-2}+7 x^{-3} \] \[ f^{\prime}(x)= \]2 answers -
11. What are all solutions to the differential equation \( \frac{d y}{d x}=\sec ^{2} x \) ? (A) \( y=\tan x+C \) (B) \( y=\sec x+C \) (C) \( y=\frac{1}{3} \sec ^{3} x+C \) (D) \( y=2 \sec ^{2} x \tan2 answers -
14. If \( \frac{d y}{d x}=\sin x \cos ^{2} x \) and if \( y=0 \) when \( x=\frac{\pi}{2} \), what is the value of \( y \) when \( x=0 \) ? (A) -1 (B) \( -\frac{1}{3} \) (C) 0 (D) \( \frac{1}{3} \) (E)2 answers -
2 answers
-
(1 point) Let \( f(x, y, z)=\frac{x^{2}-6 y^{2}}{y^{2}+3 z^{2}} \). Then \[ \begin{array}{l} f_{x}(x, y, z)= \\ f_{y}(x, y, z)= \\ f_{z}(x, y, z)= \end{array} \]2 answers -
solve the questions fully please
2. \( y=\left(3 x^{4}+x^{2}+10\right)^{3} \) 3. \( y=\sqrt{-5 x^{2}-7 x} \) 4. \( y=\sqrt[4]{x^{5}-2 x} \) 5. \( y=\left[\left(x^{2}-3 x\right)^{4}+x^{2}\right]^{3} \) 6. \( y=\sqrt{1+\sqrt{8 x-1}} \)0 answers -
2 answers
-
2 answers
-
2 answers
-
around y axis volume revolved around y axis
11. \( y=2 x-1, \quad y=\sqrt{x}, \quad x=0 \) 12. \( y=3 /(2 \sqrt{x}), \quad y=0, \quad x=1, \quad x=4 \)2 answers -
Need help please.
Find \( y^{\prime} \) if \( x^{y}=y^{x} \). \[ y^{\prime}=\frac{\ln (y)-\frac{y}{2}}{\ln (x)-\frac{2}{y}} \]2 answers -
Find \( y^{\prime} \) and \( y^{\prime \prime} \) by implicit differentiation. \[ \begin{array}{l} 4 x^{3}-3 y^{3}=8 \\ y^{\prime}= \frac{4 x^{2}}{3 y^{2}} \\ y^{\prime \prime}=\frac{8 x y-x}{3 y^{3}}2 answers -
Find the gradient of the given function. 1. \( f(x, y, z)=x^{2} \) 5. \( f(x, y, z)=y z^{2} /\left(1+x^{2}\right) \) 2. \( f(x, y, z)=x^{2}+y^{3}-z^{4} \) 6. \( f(x, y, z)=1 /\left(x^{2}+y^{2}+z^{2}\r2 answers -
2 answers
-
2 answers
-
Find curl F. F(x, y, z) = y cos(x)i + x sin(y)j - 9k
Find curl F. \[ F(x, y, z)=y \cos (x) \mathbf{i}+x \sin (y) \mathbf{j}-9 \mathbf{k} \]2 answers -
(3) solve the given initial value problem. a) \( 3 y^{\prime \prime}+11 y^{\prime}-4 y=0 \quad y(0)=3, \quad y^{\prime}(0)=2 \) b) \( y^{\prime \prime}+9 y=0 \quad y(0)=5, \quad y^{\prime}(0)=6 \)2 answers -
Solve the differential equation. \[ \begin{array}{l} 25 y^{\prime \prime}-40 y^{\prime}+16 y=0 \\ y=C e^{(4 / 5) x} \\ y=\left(C_{1}+C_{2} x\right) e^{(4 / 5) x} \\ y=C_{1} e^{(4 / 5) x}+C_{2} e^{(-42 answers -
Evaluate the integral
\( A=\int_{0}^{1} \int_{-x}^{\sqrt{x}} d y d x+\int_{0}^{1} \int_{x-2 \mid}^{\sqrt{x}} d y d x \)2 answers -
6. Solve the initial-value problem: (a) \( \left(5\right. \) marks) \( y^{\prime}=\frac{x y \sin x}{y+1}, y(0)=1 \). (b) (5 marks) \( 2 x y^{\prime}+y=6 x, x>0, y(4)=20 \).2 answers -
31. \( \int \frac{x}{\left(x^{2}+2 x+2\right)^{2}} d x \) 32. \( \int \frac{x^{\frac{1}{3}}}{x^{\frac{1}{2}}+x^{\frac{1}{4}}} d x \) 33. \( \int \frac{1}{1+\cos 2 x} d x \) 34. \( \int \frac{\sec x}{\2 answers -
Determine \( h=h(x, y) \) so that 1. \( h(x, y)=24 x y^{3} \) \[ \frac{\partial f}{\partial x}=\frac{h(x, y)}{\left(2 x^{2}+3 y^{2}\right)^{2}} \] 2. \( h(x, y)=12 x y^{2} \) 3. \( h(x, y)=12 x y^{3}2 answers -
2 answers
-
Help with 1-4. Find the gradient of the function.
1. \( f(x, y, z)=x^{2} \) 2. \( f(x, y, z)=x^{2}+y^{3}-z^{4} \) 3. \( f(x, y, z)=e^{x+y+z} \) 4. \( f(x, y, z)=\cos (x+y)+\sin (y+z) \)2 answers -
Help with 5-8. Find the gradient of the function.
5. \( f(x, y, z)=y z^{2} /\left(1+x^{2}\right) \) 6. \( f(x, y, z)=1 /\left(x^{2}+y^{2}+z^{2}\right) \) 7. \( f(x, y, z)=\sqrt{x^{2}+y^{2}+z^{2}} \) 8. \( f(x, y, z)=x e^{y} \sin z \)2 answers