JHU Future Scholars

what is the formula for integration by polynomial substitution?

In an integral

In an integral

In an integral

integrals that have:

integrals that have:

|x| > 1

definition of continuity at a point (epsilon-delta definition)

a function '“f” is continuous at “c” if for every c > 0, there exists a Delta > 0 such that if |x - c| < Delta, then |f(x)-f(C)| < epsilon. this means you can make f(x) arbitrarily close to f(C) by keeping x sufficiently close to C.

definition of differentiability at a point

Taylor Series definition

Sin(A)*Sin(B)

Cos(A)*Cos(B)

Sin(a)*cos(b)

what does it mean for a function f(x) to be continuous at x = a?

f(x) is continuous at x = a if:

1. f(a) is defined

2. lim(x→a) of f(x) exists

3. lim(x→a) of f(x) = f(a)

what is epsilon mean regarding the definition of continuity at a point epsilon delta definition?

epsilon represents how close f(x) is to the limit value regarding vertical distance

what is delta mean regarding the definition of continuity at a point epsilon delta definition?

delta represents how close “x” must be to the input value regarding horizontal distance

Fundamental theorem of calculus part 1

If F(x)=\int_a^x f(t)\,dt, then F'(x)=f(x).

Fundamental theorem of calculus part 2

If F'(x)=f(x), then \int_a^b f(x)\,dx=F(b)-F(a).