## 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