What is calculus?

1 Answer
Dec 19, 2017

Look below

Explanation:

Calculus is sectioned off into 3 parts, differential calculus (calculus 1), integral calculus (calculus 2), and multi variable calculus (calculus 3).

calculus 1:
This deals with the limits (for ex. #lim_{x->0} 3x^2#) and the discontinuities of the limits from equations (mainly expressions) and graphs.
#lim_{x->0} cscx# does not exist.
graph{csc(x) [-10, 10, -5, 5]}

and it also deals with derivatives of simple and complex functions.

#d/dx 2x^2 = 4x#

derivative rules:

power rule:
the power rule is used by the formula #nx^{n-1}#

quotient rule
the quotient rule is used by the formula #\frac{f'g-g'x}{g^2}#
note: use quotient rule if there is a fraction.

product rule
#f'g+g'f#

the #d/dx x = 1# and the #d/dx n=0#, n being a constant

you can also use the definition of a limit

#lim_{x->0} \frac{f(x+h)+f(x)}{h}#

derivatives of trig functions

trig is used a lot, so as much as the derivatives.

#d/dxsin(x)=cos(x)# this goes on a loop back to #sin(x)#
#d/dxcos(x)=-sin(x)#
#d/dx-sin(x)=-cos(x)#
#d/dxtan(x)=sec^2(x)#
#d/dx(secx)=secx*tanx#
#d/dxcsc=-csc*cot#
#d/dxcot=-csc#

calculus 2

since my computer can handle me typing this much, ill talk about calculus 2 definite integrals here, and indefinite integrals and calculus 3 in the comments.

definite integrals are in the form #int_a^b f(x)dx#.