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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Differentiate the equation z = 2x + 3y + c with respect to x.
💡 Hint: Focus on how differentiating with respect to x only affects terms with x.
Question 2
Easy
Given z = kx + my + b, identify the method to remove arbitrary constants.
💡 Hint: Remember to differentiate the entire equation.
Practice 4 more questions and get performance evaluation
Interactive Quizzes
Engage in quick quizzes to reinforce what you've learned and check your comprehension.
Question 1
What do we eliminate to form a PDE from a relation with arbitrary constants?
- Variables
- Constants
- Functions
💡 Hint: Think about what we are changing when we differentiate.
Question 2
True or False: Arbitrary functions can also be eliminated when forming PDEs.
- True
- False
💡 Hint: Recall the definitions of arbitrary functions.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given the relation z = a * sin(x) + b * cos(y), differentiate and form a PDE by eliminating constants.
💡 Hint: What happens if you set the relationship to zero?
Question 2
For z = f(x² + y²) + d*e^(x+y), derive a PDE by eliminating the function f and constant d.
💡 Hint: Pay attention to your differentiation steps!
Challenge and get performance evaluation