table

glossary

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1.
absolute max or min: occurs at interior point or endpoint, a local max or min can be a global max or min

2.
cos ((pi/2)-x): sinx

3.
d/dx (sec x): sec(x) tan(x)

4.
d/dx (tan x): sec^2 (x)

5.
d/dx cot(x): csc^2(x)

6.
essential discontinuity: where the curve has a vertical asymptote

7.
for a function to be continuous: f(c) must exist, lim x->c f(x) exists, lim x->c f(x) = f(c)

8.
jump discontinuity: where the curve breaks at a place and starts somewhere else

9.
lim x-> 0 (cosx-1)/x: 0

10.
lim x-> 0 sinax / sinbx: a/b

11.
lim x->0 sin ax/x: a

12.
lim x->0 sinx/x: 1

13.
local maximum or minimum: the curve has a horizontal tangent at that point, but its not hte highest or lowest value the function reaches

14.
mean value theorem: if y = f(x) is continuous on [a,b] and differentiable everywhere on the interval (a,b) then there is at least one number c between a and b such that f(b) -f(a) / b-a = f'(c)

15.
point discontinuity: when the curve has a hole

16.
point slope equation: y-y1 = m(x-x1)

17.
removable discontinuity: when a rational expression with common factor in numerator and denominator

18.
sin ((pi/2) -x): cos x

19.
sin (a + b): sin(a)cos(b) + cos(a)sin(b)

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