Quiz: Calculus in Day-to-Day Life Select one answer per question, then click Submit. 1) Calculus is primarily the study of: A) Static shapes only B) Change and accumulation C) Randomness without structure D) Discrete logic exclusively Calculus quantifies change and totals. 2) Differentiation measures: A) Total accumulation B) Instantaneous rate of change C) Only average change D) Surface area Derivatives capture “how fast” at an instant. 3) Integration is used to compute: A) Slopes at points B) Instantaneous velocity C) Totals such as area, volume, or energy D) Only probabilities in discrete cases Integrals add up small pieces into totals. 4) Which chain is correct in classical mechanics? A) Position is derivative of velocity; velocity is derivative of acceleration B) Velocity is derivative of position; acceleration is derivative of velocity C) Acceleration is integral of position D) Position is integral of acceleration twice per second v = dx/dt; a = dv/dt. 5) In pharmacokinetics, differential equations help: A) Select pill color B) Describe absorption and elimination to set dosage C) Replace clinical trials D) Eliminate measurement error Models guide safe and effective dosing. 6) In economics, “marginal” typically refers to: A) Total revenue B) Derivative of a function, such as cost or revenue C) Integral of utility D) Fixed overheads “Marginal” is the instantaneous rate—i.e., derivative. 7) Overfitting is to ML as which is to calculus-based modeling pitfalls? A) Ignoring boundary conditions in differential equations B) Using units consistently C) Checking dimensional analysis D) Applying continuity Bad boundary conditions break physical realism in solutions. 8) In environmental modeling, integrals compute: A) Local slopes only B) Total emissions or cumulative impacts over time C) Exact weather daily D) Political outcomes Integration accumulates rates into totals. 9) In computer graphics, calculus helps with: A) Color naming B) Light transport, shading, and smooth motion C) File compression formats D) Keyboard input handling Derivatives and integrals underpin rendering and animation. 10) A broad societal impact of calculus is that it: A) Replaced statistics entirely B) Enabled dynamic modeling and prediction across sciences C) Applies only to astronomy D) Is unused in modern technology It’s foundational to modern science and engineering. Submit Reset