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What is Calculus?

Calculus is a branch of mathematics that studies how things change.

Why do we need Calculus?

Calculus develops the ability to think and solve problems.

Everyday uses of Calculus:

physics

engineering

economics

statistics

medicine

What are the 2 kinds of Calculus?

Differential: rates of change and slopes of curves

Integral: area under the curve

Limits

In calculus, a limit is the value that a function approaches a value.

For the limit to exist, the limit from the left must equal the limit from the right and equal the point.

Continuity

L’Hospital’s Rule:

A function is continuous at a point x = a if:

The function is defined at x = a

f(a) equals a real number

The limit of the function as x approaches a exists

The limit of the function as x approaches a is equal to the function value at x = a.

When you have a 0/0 (indeterminate) you can use L'Hospital's Rule