Calculus Archive: Questions from September 14, 2022
-
Solve for \( y: \frac{d y}{d x}=\frac{e^{-2 x}}{1+e^{-2 x}} \) a. \( y=\frac{1}{2} \sin e^{-2 x}+C \) b. \( y=-2 \arctan e^{-2 x}+C \) c. \( y=-\frac{1}{2} \ln \left(1+e^{-2 x}\right)+C \) d. \( y=2 x1 answer -
a) \( \quad y=\frac{\cos x}{1-x} \) \( y^{\prime}=1 \) b) \( y=\frac{x^{2}}{1+2 x} \) \( y^{\prime}=1 \) c) \( y=\frac{e^{x}}{1+e^{-x}} \) \( y^{\prime}=1 \) a) \( \frac{x^{2}}{4+x} \) b) \( \sqrt{x}2 answers -
1. \( y=-x^{2}+3 \) 2. \( y=\frac{x^{3}}{3}-x \) 3. \( y=2 x+1 \) 4. \( y=x^{2}+x+1 \) 5. \( y=\frac{x^{3}}{3}+\frac{x^{2}}{2}+x \) 6. \( y=1-x+x^{2}-x^{3} \)1 answer -
\[ y=\left(x^{3}+x+1\right)\left(x^{4}+x^{2}+1\right) \] \[ y=\left(x^{2}+1\right)\left(x^{3}+1\right) \] \[ y=\frac{2 x+5}{3 x-2} \] \( y=\frac{x^{2}+5 x-1}{x^{2}} \) 5. \( y=\frac{(x-1)\left(x^{2}+x2 answers -
7-12 thanks!
\[ y=\left(x^{3}+x+1\right)\left(x^{4}+x^{2}+1\right) \] \[ y=\left(x^{2}+1\right)\left(x^{3}+1\right) \] \[ y=\frac{2 x+5}{3 x-2} \] \( y=\frac{x^{2}+5 x-1}{x^{2}} \) 5. \( y=\frac{(x-1)\left(x^{2}+x1 answer -
1 answer
-
Determine whether to apply the Intermediate Value Theorem to justify the existence of a real number c in I such that f(c) = L
Sea \( f(x)=\ln x-e^{-x}, I=(0,1) \) y \( L=0 \) Determina si aplica el Teorema de Valor Intermedio para justificar la existencia de un número real \( c \) en \( I \) talque \( f(c)=L \). Seleccione1 answer -
Given \( g(x)=\frac{3 \sin x-3 \cos x}{\sin x+\cos x} \). Find \( g^{\prime}(x) \) \[ \begin{array}{l} 6 \\ \frac{3}{\cos x-\sin x} \\ \frac{6}{(\sin x+\cos x)^{2}} \\ \frac{3 \cos x+3 \sin x}{(\sin x2 answers -
1 answer
-
Next to each DE below, place the letters of all applicable properties. (a) Linear (b) Nonlinear (c) Separable (d) Homogeneous i) \( y^{\prime}=\frac{x^{2}-5 x y}{3 x y} \) ii) \( y^{\prime}=\frac{y}{x1 answer -
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- ---------------
Describe the domain and range of the function. \[ f(x, y)=\ln (x y-3) \] Domain: \[ \begin{array}{l} \{(x, y): x y>3\} \\ \{(x, y): x>3, y>3\} \\ \{(x, y): x y \geq 3\} \end{array} \] \( \{(x, y): x \2 answers -
please #8,26,27
3-30 Differentiate. 3. \( y=\left(4 x^{2}+3\right)(2 x+5) \) 4. \( y=\left(10 x^{2}+7 x-2\right)\left(2-x^{2}\right) \) 5. \( y=x^{3} e^{y} \) 6. \( y=\left(e^{x}+2\right)\left(2 e^{x}-1\right) \) 7.1 answer -
#16 please
3-30 Differentiate. 3. \( y=\left(4 x^{2}+3\right)(2 x+5) \) 4. \( y=\left(10 x^{2}+7 x-2\right)\left(2-x^{2}\right) \) 5. \( y=x^{3} e^{y} \) 6. \( y=\left(e^{x}+2\right)\left(2 e^{x}-1\right) \) 7.1 answer -
1 answer
-
#26,27
3-30 Differentiate. 3. \( y=\left(4 x^{2}+3\right)(2 x+5) \) 4. \( y=\left(10 x^{2}+7 x-2\right)\left(2-x^{2}\right) \) 5. \( y=x^{3} e^{y} \) 6. \( y=\left(e^{x}+2\right)\left(2 e^{x}-1\right) \) 7.1 answer -
1 answer
-
Considere el límite \( \lim _{x \rightarrow 0^{+}}(\cos x)^{1 / x^{2}} \) a. Use una calculadora gráfica para hallar el límite. b. Encuentre el límite analíticamente.1 answer -
For the function \( y=3 x^{5} \), find \( \frac{d^{4} y}{d x^{4}} \). \[ \frac{d^{4} y}{d x^{4}}= \]1 answer -
1 answer
-
\( \lim _{h \rightarrow 0} \frac{(2+h)^{3}+\sin \left[\frac{\pi(2+h)}{12}\right]-\frac{17}{2}}{h}= \)1 answer -
1 answer
-
c) Suppose \( g(x, y)=\frac{1}{3} y \ln x+\frac{2}{3} x \ln y \) i) What are \( g_{x}(x, y) \) and \( g_{y}(x, y) \) ? ii) Find \( g_{x y}(x, y) \) and \( g_{y x}(x, y) \).2 answers -
8. Next to each DE below, place the letters of all applicable properties. (a) Linear (b) Nonlinear (c) Separable (d) Homogeneous i) \( y^{\prime}=\frac{x^{2}-5 x y}{3 x y} \) ii) \( y^{\prime}=\frac{y1 answer