AP Calc AB Formulas

¡Supera tus tareas y exámenes ahora con Quizwiz!

Definition of the derivative

lim h->0 (f(x+h) - f(x))/h

Special Cosine Limit

lim x->0 (1-cosx)/x = 0

Special Sine Limit

lim x->0 sinx/x = 1

[int] 1/x dx =

ln x + c

[int] secx dx =

ln|secx + tanx| + c

[int] cotx dx =

ln|sinx| + c

Volume (disk method)

pi [int](a,b) [(outside/upper)^2 - (inside/lower)^2] dx or dy

d/dx(tanx) =

sec^2(x)

[int] secxtanx dx =

secx + c

d/dx(secx) =

secxtanx

[int] cosx dx =

sinx + c

[int] sec^2 (x) dx =

tanx + c

Second Fundamental Theorem of Calculus

d/dx[int](g(x),a) f(t) dt = f(g(x)) * g'(x)

d/dx(e^x) =

e^x

[int] e^x dx =

e^x + c

[int] a^x dx =

((a^x)/ln a) + c

d/dx(a^x) =

(a^x)(ln a)

d/dx(arccotx) =

-1/(1+x^2)

d/dx(arccosx) =

-1/sqrt(1-x^2)

d/dx(arccscx) =

-1/|x|sqrt(x^2 -1)

[int] sinx dx =

-cosx + c

[int] csc^2 (x) dx =

-cotx + c

d/dx(cotx) =

-csc^2(x)

[int] cscxcotx dx =

-cscx + c

d/dx(cscx) =

-cscxcotx

[int] tanx dx =

-ln|cosx| + c

[int] cscx dx =

-ln|cscx + cotx| + c

d/dx(cosx) =

-sinx

d/dx(arctanx) =

1/(1+x^2)

Average value

1/(b-a) [int] f(x) dx

Derivative of an inverse function (if g is the inverse of f)

1/(f'(g(x)))

d/dx(log base a x) =

1/(x ln a)

d/dx(arcsinx) =

1/sqrt(1-x^2)

d/dx(ln x) =

1/x

d/dx(arcsecx) =

1/|x|sqrt(x^2 -1)

Intermediate Value Theorem

If f is continuous for all x on the closed interval [a,b] and k is any number between f(a) and f(b), then there is a number x=c in (a,b) such that f(c) = k

Mean Value Theorem

If f is differentiable for all values of x on the open interval (a,b) and f is continuous at x=a and x=b, then there is at least one number c in (a,b) such that f'(c) = (f(b)-f(a))/(b-a)

L'Hôpital's Rule

If lim x->a f(x)/g(x) is 0/0, then lim x->a f(x)/g(x) = lim x->a f'(x)/g'(x)

Instantaneous rate of change

Take the derivative

Trapezoidal Rule

[int](a,b) f(x) dx = (1/2)((b-a)/n)[f(x0) + 2f(x1) +...+ 2f(x(n-1)) + f(xn)]

Fundamental Theorem of Calculus

[int](a,b) f(x) dx = F(b)-F(a) where F'(x) = f(x)

[int] 1/x(sqrt(x^2 -1)) dx =

arcsecx + c

[int] 1/sqrt(1-x^2) dx =

arcsinx + c

[int] 1/(1+x^2) dx =

arctanx + c

Average rate of change

change in _/interval

d/dx(sinx) =

cosx


Conjuntos de estudio relacionados

Overview of the Neurons, Neuronal Signaling, and Neural Networks (Part I)

View Set

acuphysiology Foot shaoyang GB Channel

View Set

Intro to Networks ch 9: Transport Layer

View Set

Bone Marrow, Cytochemical, QC and QA,

View Set

Chapter 61: Management of Patients with Neurologic Dysfunction

View Set

Chapter 2.3.3 Practice Questions

View Set