Advanced Math Archive: Questions from May 02, 2023
-
1 answer
-
1. Determine the derivatives of the following functions: (i) f(x) = csc(x) (ii) g(x) = √2x cos(x) tan (3x) sin(x) (iv) k(x) = cos(x²) + cos² (x) (v) m(x) = (x³ + tanª (vi) p(x) = ecos² (-x) (vi
1. Determine the derivatives of the following functions: (i) \( f(x)=\csc (x) \) (ii) \( g(x)=\sqrt{2 x} \cos (\pi x) \) (iii) \( h(x)=\frac{\tan (3 x)}{\sin (x)} \) (iv) \( k(x)=\cos \left(x^{2}\righ2 answers -
\[ g(x)=(f \circ 3 f \circ 4 f)(x)=f(3 f(4 f(x))) \] Determine \( g^{\prime}(3) \), given \( f(3)=1, f(4)=1, f^{\prime}(3)=2 \) and \( f^{\prime}(4)=3 \).2 answers -
El campo de valores de la función definida por la gráfica es: Select one: a. \( (-2,3] \) b. Ninguna de las otras alternativas c. \( \mid 3,-1) \cup(0,3) \) d. \( (3,-1|\cup| 0,3 \mid \) e. \( (2,3)2 answers -
2 answers
-
2 answers
-
0 answers
-
3. Solve the following IVP: \[ y^{\prime \prime}+y=f(t), \quad y(0)=1, \quad y^{\prime}(0)=0, \quad f(t)=\left\{\begin{array}{ll} \frac{1}{2} & 0 \leq 12 answers -
Maximize \( f=3 x+y \) subject to \[ \begin{array}{l} 2 x+y \leq 6 \\ 6 x+y \leq 14 \\ x \geq 0, y \geq 0 . \end{array} \] \[ f= \]2 answers -
3. Solve the differential equation (Ch.8, Sec. 13, No. 28) \[ y y^{\prime \prime}+y^{\prime 2}+4=0 \] \[ y=3, y^{\prime}=0 \text { when } x=1 \]2 answers -
0 answers
-
2 answers
-
Definamos la relación \( E \) sobre \( \mathbb{N}^{\mathbb{N}} \) por la regla \[ f E g \leftrightarrow \exists m \in \mathbb{N}[\forall n \in \mathbb{N}[(n>m) \rightarrow f(n)=g(n)]] \] En palabras:2 answers