diff --git a/source/recitations/calculus-review.ptx b/source/recitations/calculus-review.ptx index f3e0ff0..bc2f963 100644 --- a/source/recitations/calculus-review.ptx +++ b/source/recitations/calculus-review.ptx @@ -12,14 +12,71 @@

- +

The Power Rule for derivatives states: - + \frac{d}{dx}\left( x^n \right) =

+ + +

+ The Power Rule for antiderivatives states: + + \int\left( x^n \right)\ dx = + +

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+
+ + +

+ Practice with the following derivatives: + + \frac{d}{dx}\left( 2x^2 + x^{-3} + 4\sqrt{x} \right) \amp = + \frac{d}{dx}\left( \frac{1}{x} + 3e^{2x} + x^e + \pi^e \right) \amp = + +

+
+
+ + +

+ Practice with the following antiderivatives: + + \int 2x^2 + x^{-3} + 4\sqrt{x} \ dx \amp = + \int \frac{1}{x} + 3e^{2x} + x^e + \pi^e \ dx \amp = + +

+
+
+ + + +

+ If F(x) is an antiderivative of f(x)i.e., if F'(x) = f(x)then the Fundamental Theorem of Calculus (FTC) says: + + \int_a^b f(x)\ dx = F(x)\bigg|_a^b = F(b) - F(a). + + If f(x) is a probability density function (don't worry about what that means for now), then integrals such as \int_a^b f(x)\ dx are used to calculate certain probabilities, and so are function values of the form F(x). +

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+
+ + + +

+ Practice with the following integrals: + + \int_0^1 \frac{3}{2} x^{3/2} \ dx \amp = + \int_0^x 3e^{-3t} \ dt \amp = + +

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+ \ No newline at end of file