Calculus Archive: Questions from August 12, 2022
-
Find \( \frac{d y}{d x} \) for each of the following: (a) \( y=\frac{\sqrt{x^{2}+1}-\sqrt{x^{2}-1}}{\sqrt{x^{2}+1}+\sqrt{x^{2}-1}} \) (b) \( y=x^{e}(2 x+3)^{4} \log _{7}\left(5 e^{x}\right) \) (c) \(1 answer -
Compute the matrix of partial derivatives of the function \( f: \mathbb{R}^{3} \longrightarrow \mathbb{R}^{2}, f(x, y, z)=\left(5 x+9 e^{2}+8 y, 5 y x^{2}\right) \) and select the correct answer from1 answer -
1 answer
-
(5 points) Find the partial derivatives of the function \[ f(x, y)=x y e^{-5 y} \] \( f_{x}(x, y) \) \[ f_{y}(x, y)= \] \[ f_{x y}(x, y) \] \[ f_{y x}(x, y)= \]1 answer -
1. Using properties of logarithms, determine the value of the constants \( a, b \), and \( c \) so that \[ f(x)=a \ln (x-2)-b \ln (x-3)-c \ln (x-5) \] \[ a=\ldots \quad ; \quad ; \quad \square= \] 2.1 answer -
help with these please
Find the \( \iiint_{Q} f(x, y, z) d V \) A. \( Q=\left\{(x, y, z) \mid\left(x^{2}+y^{2}+z^{2}=4\right.\right. \) and \( \left.z=x^{2}+y^{2}, f(x, y, z)=x+y\right\} \) B. \( Q=\left\{(x, y, z)\left\{\l1 answer -
(1 point) Given \[ \mathbf{F}(x, y, z)=(7 x+y z) \mathbf{i}+(y-x z) \mathbf{j}+(z+4 x y) \mathbf{k} \] Calculate1 answer -
1 answer
-
1 answer
-
Let \( f(x, y)=5 e^{6 x} \sin (3 y) \) \( \frac{\partial f}{\partial x}= \) \( \frac{\partial f}{\partial y}=\mid \) Given \( f(x, y)=12 \sqrt{4 x^{6}+7 y+5 x y^{5}} \), f \[ \begin{array}{l} f_{x}(x1 answer -
1) \( \lim _{x \rightarrow-2^{-}} f(x)= \) 2) \( \lim _{x \rightarrow-2^{+}} f(x)= \) 3) \( \lim _{x \rightarrow 0} f(x)= \) 4) \( \lim _{x \rightarrow 2} f(x)= \) 5) \( \lim _{x \rightarrow-2} f(x)=1 answer -
1 answer