CALCULUS FORMULAS
Calculus is a field of mathematics concerned with the study of ‘Rate of Change’ and its application to solving equations. It is divided into two primary branches: Differential Calculus, which deals with rates of change and slopes of curves, and Integral Calculus, which deals with accumulation of quantities and areas under and between curves.
CALCULUS : DERIVATIVES AND LIMITS
The derivative is a method of defining how the output of an expression varies as the inputs vary.
The limit is a technique for evaluating expressions when an input approaches a value. This value can be any point on the number line, and limits are frequently assessed when an argument approaches or deviates from infinity or minus infinity. The function approaches the value L as x approaches the value c, according to the formula following
BASIC PROPERTIES
PROPERTIES OF LIMITS
LIMIT EVALUATION +∞
MEAN VALUE THEOREM
if f differentiable on the interval (a, b) and continues at the end points there exists a c in a (a, b) such that
QOUTIENT RULE
CHAIN RULE
POWER RULE
PRODUCT RULE
DERIVATIVE DEFINITION
COMMON DERIVATIVES
LIMIT EVALUATION METHOD FACTOR AND CANCEL
L ‘HOPITAL’S RULE
CHAIN RULE & OTHER EXAMPLES
CALCULUS: INTEGRALS
COMMON INTEGRALS
TRIG SUBSTITUTIONS
INTEGRATION BY PARTS
APPROXIMATING DEFINITE INTEGRALS
Left -hand and right-hand rectangle approximation
Midpoint Rule
Trapezoid Rule
INTEGRATION PROPERTIES
INTEGRATION BY SUBSTITUTION
where u= g (x) and du = g’ (x) dx
DEFINITE INTEGRAL DEFINITION
where f is continuous on [a, b] and F’ = f
FUNDAMENTAL THEOREM OF CALCULUS
where f is continuous on [a, b] and F’ = f
L ‘HOPITAL’S RULE