null
US
Iniciar Sesión
Regístrate Gratis
Registro
Hemos detectado que no tienes habilitado Javascript en tu navegador. La naturaleza dinámica de nuestro sitio requiere que Javascript esté habilitado para un funcionamiento adecuado. Por favor lee nuestros
términos y condiciones
para más información.
Siguiente
Copiar y Editar
¡Debes iniciar sesión para completar esta acción!
Regístrate gratis
1769425
Calculus I
Descripción
Mapa Mental sobre Calculus I, creado por GraceEChem el 08/12/2014.
Sin etiquetas
math 111 - university calculus i
calculus 1
Mapa Mental por
GraceEChem
, actualizado hace más de 1 año
Más
Menos
Creado por
GraceEChem
hace casi 10 años
629
19
0
Resumen del Recurso
Calculus I
Limits
Infinite limits
Divide top and bottom by biggest power
1/x^n = 0
Finite limits
Continuous, plug in constant
0/0 is your answer?
Factor and Simplify
Derivatives
Product Rule
(fg)' = f'g+g'f
Quotient Rule
(f/g)' = (f'g - g'f) / g^2
Power Rule for Functions
(f^n)' = nf^(n-1)f'
Chain Rule
dy/dx = (dy/du)(du/dx)
for y=y(u) and u=u(x)
[f(g(x)]' = f'(g(x))g'(x)
Finding 2nd Derivative
just take the derivative of the derivative
f(x) = e^x, f'(x) = e^x
f(x) = ln x, f'(x) =1/x
g(x) = loga(x), g'(x) = (1/ln a)(1/x)
f'(x) = ln(a)a^x
Chain Rule and Logs
g(x) = ln(f(x))
f'(x)/f(x)
ln(x) + 1/x (x')
Marginal Analysis/Linear Approximation
f(x+delta x) ~= f(x) + delta x(f'(x))
or Marginal Cost = C'(x)
Implicit Differentiation
Treat x as x and y as f(x), give derivative of y w/respect to x
Differentiate both sides w/respect to x with y as f(x)
Chain rule, differentiating terms with y
Solve for dy/dx in terms of x and y
Increasing/Decreasing Functions
Use 1st Derivative
Test points @ f'(x) = 0
Plug test points into f'(x)
And where f'(x) does not exist
CRITICAL POINTS!
Concavity
Use f''(x)
Test points @ f''(x) = 0
And where f''(x) does not exist
Inflection point where concavity changes
Positive/Negative
Test points on f(x)
Optimization
x = c is critical point if f'(c) = 0
x = c relative min/max if f'(c) changes sign
x = c abolute min/max
Closed Interval
find where f'(x)=0
plug those points into f(x)
compare against interval points for absolute max/min
Open Interval
find one critical point, where f'(x)=0
this shows concavity
Exponents
Compound interest
Yearly
P(t) = P(1+r)^t
Monthly
P(t) = P(1+r/12)^12t
Continuously
P(t) = Pe^rt
Mostrar resumen completo
Ocultar resumen completo
¿Quieres crear tus propios
Mapas Mentales
gratis
con GoConqr?
Más información
.
Similar
Limits AP Calculus
lakelife62
Calculus & Integral 1 - Known limits
Bassam Mansour
Basic Derivative Rules
Bill Andersen
Calculus
natz994
Integration Techniques
Rob Grondahl
Calculus II Improper Integrals
Anthony Campos
Techniques of Integration
hamidymuhammad
STRATEGY OF INTEGRATION
intan_syahirah97
Series Strategy
Rob Grondahl
Derivadas
Roxy Hughes
Mathematicalproving
Sharifah Huda
Explorar la Librería