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Monday, March 31, 2014

Finding Equation - Curve, 4

Category: Differential Equations, Integral Calculus, Analytic Geometry, Algebra

"Published in Vacaville, California, USA"

Find the equation of a curve having the given slope that passes through the indicated point:


Solution:

The slope of a curve is equal to the first derivative of a curve with respect to x. In this case, y' = dy/dx. Let's consider the given slope of a curve



Multiply both sides of the equation by dx, we have  




Integrate on both sides of the equation, we have   






In order to get the value of arbitrary constant, substitute the value of the given point which is P(2, -5) to the above equation, we have  






Therefore, the equation of a curve is   


  

Sunday, March 30, 2014

Finding Equation - Curve, 3

Category: Differential Equations, Integral Calculus, Analytic Geometry, Algebra

"Published in Vacaville, California, USA"

Find the equation of a curve having the given slope that passes through the indicated point:


Solution:

The slope of a curve is equal to the first derivative of a curve with respect to x. In this case, y' = dy/dx. Let's consider the given slope of a curve



Multiply both sides of the equation by dx, we have 




Integrate on both sides of the equation, we have  






In order to get the value of arbitrary constant, substitute the value of the given point which is P(1, 1) to the above equation, we have  








Therefore, the equation of a curve is  


 

Saturday, March 29, 2014

Finding Equation - Curve, 2

Category: Differential Equations, Integral Calculus, Analytic Geometry, Algebra

"Published in Vacaville, California, USA"

Find the equation of a curve having the given slope that passes through the indicated point:


Solution:

The slope of a curve is equal to the first derivative of a curve with respect to x. In this case, y' = dy/dx. Let's consider the given slope of a curve



Multiply both sides of the equation by dx, we have




Integrate on both sides of the equation, we have 






In order to get the value of arbitrary constant, substitute the value of the given point which is P(3, -6) to the above equation, we have 






Therefore, the equation of a curve is