calc bc

Vertical asymptote

The line that a function can’t cross

Horizontal asymptote

The end behavior of a function

Linearization

Replace h with dx and remove the limit

f(x+dx)≈f(x)+f’(x)

L’Hospital’s Rule

If a limit gives 0/0 or inf/inf then we can take derivative of numerator and dominator and try again

Intervals of increase and decrease

Take the first derivative of the function and set it equal to zero

Function concavity

If the second derivative of a function is greater than 0, then the function is concave up, meaning that it’s increasing it decreasing by an increasing rate. And if a second derivative of a function is less than 0, function is concave down.

Riemann left sum

Change in top row multiplied by the bottom number excluding the last one on the right

Riemann right sum

Change in top row multiplied by the bottom number excluding the last one on the left

Trapezoidal sum

Slope fields

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Differential equations(SIPPY)

•S: separate dx and dy on other sides

•I: integrate

•P: plus C

•P: plug in your initial condition

•Y: solve to find y

Average value of a function with integral

Area between two curves

Find the integrals and subtract the bottom function

Memory integrals

Memory derivatives