These are my complete notes for Integral Calculus & Calculus 2, covering such topics as Definite & Indefinite Integrals, the Fundamental Theorem of Calculus, LRAM, RRAM, and MRAM, the Trapezoid Rule, Exponential Growth/Decay, Trigonometric Antidifferentiation, the Washer Method, Integration by Parts, Power Series & Infinite Series, and more.
I color-coded my notes according to their meaning - for a complete reference for each type of note, see here (also available in the sidebar). All of the knowledge present in these notes has been filtered through my personal explanations for them, the result of my attempts to understand and study them from my classes and online courses. In the unlikely event there are any egregious errors, contact me at jdlacabe@berkeley.edu.
Summary of Integral Calculus & Calculus 2 (Complete)
?. Local Linearity.
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Rule .
If you continuously zoom in at the value pi/2, you can see the graph flatten until it becomes a line. The line represents the slope of the tangent line at that point. WE can use the tangent line at that point to approximate the value of y = sin(x) for points near x = pi/2. This is called linearization.
# Linear Approximation: If f is differentiable at x=a, then the equation of the tangent line, L(x) = f(a) + f'(a)(x-a), defines the linearization of f at a. The approxijmation is called the Linear Approximation of f at the point x=a is the center of approximation.
