Advanced Math Archive: Questions from January 07, 2023
-
Differentiate the functions. a. \( \quad \mathrm{G}(\mathrm{x})=7 \mathrm{x}^{3}-5 \mathrm{x}^{2} \) b. \( f(t)=-13 t^{2}+14 t+1 \) c. \( f(x)=\frac{3\left(x^{3}-2 x\right)}{4} \) d. \( p(x)=\frac{x^{2 answers -
2. Differentiate the functions (apply product \& quotient rules if necessary). a. \( \mathrm{f}(\mathrm{x})=(3 \mathrm{x}-1)(7 \mathrm{x}+2) \) b. \( Q(x)=\left(x^{2}+3 x\right)\left(7 x^{2}-5\right)2 answers -
\( Q_{4} \) : if \( f(x)=e^{4 x}+\sin 3 x \) find \( \left.\frac{d^{82}}{d x^{82}} f(x)\right) \) \( Q_{5} \) : if \( f(x)=e^{4 x} \quad \) lind \( \lim _{y \rightarrow x} \frac{f^{(65)}(y)-f^{(55)}(x2 answers -
Solve the initial value problem: \( y^{\prime \prime \prime}-2 y^{\prime \prime}+y^{\prime}=0, y(0)=0, y^{\prime}(0)=5, y^{\prime \prime}(0)=8 \) \[ y(t)=2 e^{t}-3 t e^{t}+2 \] \( y(t)=3 e^{t}+2 t e^{2 answers -
initial value problem
Solve the initial value problem: \( y^{\prime \prime \prime}-2 y^{\prime \prime}+y^{\prime}=0, y(0)=0, y^{\prime}(0)=5, y^{\prime \prime}(0)=8 \). \[ \begin{array}{l} y(t)=2 e^{t}-3 t e^{t}+2 \\ y(t)=2 answers -
2 answers