Slope fields allow us to visualize a solution to a differential equation without actually solving the differential equation. Let’s construct a slope field to solidify this idea. 🧠
Slope fields essentially draw the slopes of line segments that go through certain points. Let’s consider the following differential equation:
The slope (m) at point (x, y), in this case, is just x + y, which we can put into a table for various coordinates:
We can use this data to draw an approximate solution to the differential equation by drawing short line segments through each point that have the corresponding slope: 🌄
To be continued in 7.4 Reasoning Using Slope Fields.
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✍️ Free Response Questions (FRQ)
👑 Unit 1: Limits & Continuity
🤓 Unit 2: Differentiation: Definition & Fundamental Properties
🤙🏽 Unit 3: Differentiation: Composite, Implicit & Inverse Functions
👀 Unit 4: Contextual Applications of the Differentiation
✨ Unit 5: Analytical Applications of Differentiation
🔥 Unit 6: Integration and Accumulation of Change
💎 Unit 7: Differential Equations
🐶 Unit 8: Applications of Integration
🦖 Unit 9: Parametric Equations, Polar Coordinates & Vector Valued Functions (BC Only)
♾ Unit 10: Infinite Sequences and Series (BC Only)
🧐 Multiple Choice Questions (MCQ)
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