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Riemann Integrable function solved Question

By SK Math Expert May 13, 2021Real AnalysisRiemann integration

Introduction : Any function that satisfies conditions of Riemann integral conditions is a Riemann integrable function. An example is solved. Question : Show that following function \[f\left(x\right)=1 , if 2≤x<32\]…

Solved Van Der Val ODE solution long term behaviour

By SK Math Expert May 13, 2021ODEsNon Linear ODEs

Introduction : Van Der Val ODE is a second order differential equation. To analyse it's solution behaviour First we convert it into a system of first order ODEs then obtained…

solved particular integral of linear ode dy/dt+cos(t)y=3cos(t)

By SK Math Expert May 13, 2021ODEsLinear ODEs

Introduction : The differential equation dy/dt+cos(t)y=3cos(t) is a linear ode. We shall apply integrating factor method to solve this. Finally using initial condition we shall get it's particular integral. Question…

Geometry aptitude question

By SK Math Expert May 12, 2021Advanced MathGeometry aptitude

Introduction : Geometry aptitude question "Two straight lines are drawn perpendicular to each other in X-Y plane. If alpha and beta are acute angles the straight line make with X-axis,…

Solved Euler Mayurma Method to solve SDE dx=(5-x)/(7-t)dt+dWt

By SK Math Expert May 9, 2021Advanced MathSDE

Introduction : In this Euler Mayurma Method is applied to solve stochastic differential equation dx=(5-x)/(7-t)dt+dWt Question : Using Euler Mayurma Method to solve SDE \[dx=\frac{5-x}{7-t}dt+dW_t\] subject to initial condition […

Find the area of a parallelogram whose base is 10 cm and height is 14 cm

By SK Math Expert May 8, 2021Advanced Mathparallelogram

Introduction : Area of a parallelogram, whose base and height are known, is calculated as follows Question: Find the area of a parallelogram whose base is 10 cm and height…

Solved Convert Van Der Pol Oscillator into system of first order ODEs

By SK Math Expert May 7, 2021Numerical AnalysisFirst order odes

Introduction : Van Der Pol Oscillator is a second order ODE. This equation is converted into a system of first order ODEs. Question : Convert Van Der Pol Oscillator \[\frac{d^2x}{dt^2}-3\left(1-x^2\right)\frac{dx}{dt}+x=0…

Solved what are vectors a and b such that aA-bB+2C=0 for given vectors A, B, C

By SK Math Expert May 7, 2021Advanced MathVector Algebra

Introduction: In this solution, we explain answer of what are vectors a and b such that aA-bB+2C=0 for given vectors A, B, C. Question: If A = (6i−8j) units, B…

Solved What are vectors a and b

By SK Math Expert May 7, 2021Advanced MathVector Algebra

Introduction: In this solution, we will determine what are vectors a and b from the given relation between them. Question : If vector c = 3i+4j and a−b =2c, a+b=4c…

Solved how to find Average velocity

By SK Math Expert May 7, 2021Advanced Mathvelocity

Introduction: in this question, we calculated average velocity. Question: Alan drives his truck on a straight road for 5.8 KM at 40 KM/h, at which point he run out of…