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Calc 1 Final
N/A
14
Mathematics
Undergraduate 1
05/01/2014

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Cards

Term
Sin(x)
Definition
Cos(x)
Term
Cos(x)
Definition
-Sin(x)
Term
Tan(x)
Definition
sec^2(x)
Term
csc(x)
Definition
-csc(x)cot(x)
Term
Sec(x)
Definition
sec(x)tan(x)
Term
cot(x)
Definition
-csc^2(x)
Term
sin^-1(x)
Definition
1/sqrt(1-x^2)
Term
tan^-1(x)
Definition
1/(1+x^2)
Term
Lim as x approaches a exists
Definition
If the right hand derivative and the left hand derivative are equal
Term
f(x) is continuous at x=a if
Definition
limit as x approaches a of f(x) equals f(x)
Term
f'(x) at x = a and its four equivalent interpretations
Definition
lim as h approaches 0 of f(a+h)-f(a)/h exists.
1. derivative at x=a
2. velocity at x=a
3. instant rate of change
4. slope
Term
Mean Value Theorem- differentiable
Definition
if f(x) is continuous over [a,b], differentiable over (a,b), then there exists some c in [a,b] such that f'(c)=f(b)-f(a)/b-a
Term
Mean Value Theorem- integrable
Definition
if f(x) is an integrable function over [a,b], then there exists some C(y-value) such that the integral from a to b = c(b-a)
Term
Fundamental Theorem of Calculus 1 and 2
Definition
FTC 1: if f(x) is continuous then the integral from 0 to x equals f(x)
FTC 2: if F(x) is any anti-derivative of f(x)then the integral of f(x) from a to b is F(b)- F(a)
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