Limits
Informal definition of limit
What is the value of the function as x approaches a value from the left and the right
What is slope of curve at a point? What is slope of tangent line? What is instantaneous rate of change?
Constant Rule: Derivative of c where c is a constant
What is 0?
Power Rule for Antiderivatives: Integral of xn dx
What is xn+1/(n+1) + C?
Point slope form of a line
What is y-y1=m(x-x1) ?
Limit as x approaches zero of sinx/x
What is 1?
Derivative of sin(x)
What is cos(x)?
Power rule: Derivative of xn
What is nxn-1?
Integral of sin(x) dx
What is -cos(x) + C ?
Different types of discontinuity
What is jump, removable, and infinite?
Limit as x approaches zero of (1-cosx)/x
What is zero?
Derivative of tan(x)
What is sec2x?
Product Rule: Derivative of f(x)g(x)
What is f'(x)g(x)+f(x)g'(x)?
What is the integral of ex dx ?
What is ex ?
Average value of f(x) on [a,b]
What is 1/(b-a) integral from a to b of f(x) dx ?
What is the limit as x approaches zero of (a sinx)/bx where a and be are constants
What is a/b ?
Derivative of ln(x)
What is 1/x?
Quotient Derivative: Derivative of f(x)/g(x)
What is (f'(x)g(x)-f(x)g'(x))/(g(x))2 ?
Integral of dx/x
What is ln|x| + C ?
Area between curves
What is integral from left to right of (top - bottom) dx ?
Limits definition of derivative
What is the limit as x approaches h of (f(x+h)-f(x))/h or limits as x approaches a of (f(x)-f(a))/(x-a)?
Derivative of inverse function
What is 1/(f'(f-1(x))?
Chain Rule: Derivative of f(g(x))
What is f'(g(x))g'(x)?
Fundamental Theorem of Calculus: Integral from a to b of f(x) dx
What is F(b)-F(a) where F is an antiderivative of f ?
Disc Method
What is integral from a to b of (pi R2 - pi r2 ) dx ?