Dabo CalcAB Sem1 FINAL Day2

Jump discontinuities occur when the left-hand limit and right-hand limit of a function at a certain point exist but are not equal, causing a 'jump' in the graph.

x = -1, 0, 1.

The integral of a function represents the area under the curve of that function on a given interval.

h'(3) represents the derivative of the function h at the point x = 3, indicating the slope of the tangent line to the graph of h at that point.

The limit of a function describes the value that the function approaches as the input approaches a certain value.

It means that as x approaches 'a', the function f(x) approaches the value 3.

The derivative is $$f'(x)=2\text{sin}(x)\text{cos}(x)$$ .

The product rule states that if you have two functions u(x) and v(x), then the derivative of their product is given by $$(uv)' = u'v + uv'$$ .

The chain rule is used to differentiate composite functions and states that if $$y = f(g(x))$$ , then $$dy/dx = f'(g(x)) * g'(x)$$ .

The derivative at a point gives the instantaneous rate of change of the function at that point, which can be interpreted as the slope of the tangent line.