Other Math Archive: Questions from October 09, 2022
-
3.36. Let \( z=x+i y \) and show that (a) \( |\sin z|^{2}=\sin ^{2} x+\sinh ^{2} y=\cosh ^{2} y-\cos ^{2} x \) (b) \( |\cos z|^{2}=\cos ^{2} x+\sinh ^{2} y=\cosh ^{2} y-\sin ^{2} x \) (c) If \( \cos x3 answers -
Fxpress the following function in the form \( |x|=u \) tiv. \[ f(c)=z^{4} \] 1. \( f(x)=\left(x^{4}-6 y^{2} y^{2}+y^{4}\right)+\left(4 x^{2} y-4 y^{3}\right) \) 1. \( f(x)=\left(x^{4}-6 x^{2} y^{2}+y^2 answers -
Find \( y^{\prime \prime} \) for \( y=\left(5+\frac{2}{x}\right)^{3} \) \[ y^{\prime \prime}= \] Find \( y^{\prime \prime} \) for \( y=e^{x^{3}}+4 x \) \[ y^{\prime \prime}= \]2 answers -
Prove or disprove the propositions: (a) \( \forall x \in \mathbb{R}, \exists y \in \mathbb{R} \cdot x=y^{3} \) (b) \( \exists y \in \mathbb{Z} \cdot \forall x \in \mathbb{N}, x>y \) (c) \( \forall x \2 answers -
2 answers
-
PLS HELP! differential equations. MATH 2065
Solve the initial value problems 1. \( y^{\prime \prime}+4 y^{\prime}+4 y=4 \cos 2 t \) \( y(0)=0, \quad y^{\prime}(0)=1 \) 2. \[ \begin{array}{l} y^{\prime \prime}+4 y^{\prime}+4 y=16 t \sin 2 t \\ y2 answers -
2 answers