Recent questions tagged numerical-methods

Consider the equation $\dfrac{d y}{d x}=\dfrac{1}{x}$The value of the integral $\int_{1}^{2} d y$ using trapezoidal method and interval $h=0.25$ is $\_\_\_\_$. (rounded o...

Consider a nonlinear algebraic equation, $e^{x}-2=0$. Using the Newton-Raphson method, with the initial guess of $x_{0}=1$, the approximated value of the root of the equa...

A fermentor is filled with medium at a rate of $1 \mathrm{~L} \mathrm{~min}^{-1}$. A leak develops at the bottom of the fermentor when the medium in the fermentor reaches...

The absolute relative error in evaluating the integral $\int_0^1 x^2 d x$ by the trapezoidal rule with the step size $0.25$ is $\%$ $\_\_\_\_\_\_\_\_$ (rounded off to $2$...

If $1000 \mathrm{bp}$ of a double-helical DNA weighs $1 \times 10^{-18} \mathrm{gm}$ and distance between two $\mathrm{bp}$ is $0.34 \mathrm{~nm}$, the total amount of DN...

Consider a nonlinear algebraic equation, $x\ln x + x – 1 = 0.$ Using the Newton-Raphson method, with the initial guess of $x_{0} = 3,$ the value of $x$ after one iteratio...

A fermentation broth of density $1000 \; \text{kg m}^{-3}$ and viscosity $10^{-3} \; \text{kg m}^{-1} \text{s}^{-1}$ is mixed in a $100\;\text{L}$ fermenter using a $0.1 ...

Consider the ordinary differential equation $\dfrac{dy}{dx} = f(x,y) = 2x^{2} – y^{2}.$ If $y(1)=1,$ the value(s) of $y(1.5),$ using the Euler’s implicit method $\left[y_...

A bacterial strain is grown in nutrient medium at $37^{\circ}\text{C}$ under aerobic conditions. The medium is inoculated with $10^{2}$ cells from a seed culture. If the ...

A sedimentation tank of height $100 \textit{ cm}$ is used in a conventional activated sludge process to separate a suspension of spherical shaped granular sludge biomass ...

$\int _{-1}^{1}\:f\left ( x \right )dx$ calculated using trapezoidal rule for the values given in the table is ______ (rounded off to $2$ decimal places).$$\begin{array}{...

A $5$ liter chemostat is fed fresh medium at $0.2$ liters/minute having a substrate concentration of $25$ grams/liter. At steady state, the outgoing stream has substrate ...