BASIC CALCULUS TERMINOLOGIES Flashcards
● one of the most important ideas or concepts in studying calculus
● the backbone of the calculus, both differential and integral calculus.
LIMITS
Ways to determine if the limit exists
○ by making the table of values of the function
○ by graphing the given function.
○ to find out whether the value of x will approach the value of the constant c, we need to specify the direction
One - Sided Limits
Left - sided limits
→ limit from the left, less than c
lim f(x) = L
x → c-
- Right - sided limits
→ limit from the right, greater than c
lim f(x) = L
x → c+
the limit exists since the values from
left and right are equal.
lim f(x) = lim f(x)
x → c- x → c+
limit does not exist since the values
from left & right are not equal.
lim f(x) ≠ lim f(x)
x → c- x → c+
SOLVE:
lim (1 + 2x)
x→ 3
→ 1 + 2 (3) → 1 + 6 = 7
different left and right limits at every integer
Greatest - integer function
limit of a constant is that constant
Theorem on Limit of Functions
○ function values decrease or increase without bounds as independent variable gets closer and closer to a certain fixed number.
Infinite Limits
if x equates to 0 and → f(x) = 1
x
If denominator equate to 0 & numerator is not 0
let exponent a be even and let exponent b be odd
Even and Odd exponents
If the highest power of x is the same in both the
numerator and denominator, then :
VII. Limits of Rational Expression as x → ∞
If the highest power of x is in the denominator…
lim f(x) = 0
x → ∞
If the highest power of x is in the numerator…
lim f(x) = ∞
x → ∞