Please enable JavaScript.
Coggle requires JavaScript to display documents.
Chapter 2 Calculus (2.5 (Dividing by very large or small #s (Any #/ very…
Chapter 2 Calculus
2.5
When x approaches ∞
Top heavy: lim h(x) = -∞ or ∞
Equal: lim g(x) = A/C
Bottom heavy: lim f(x)=0
Dividing by very large or small #s
Any #/ very big # = very small number = 0
Any #/-very small # = -very large # = -∞
Any #/very small # = Very large # = ∞
Any #/-very big # = -very small number = 0
2.4
Reasons for Discontinuity
fn has no limit
f(c) has no value
f(c) does not equal the limit
Cusp = sharp point on the graph
Cannot find derivatives of a function at a cusp
2.2
Solve for any value of positive value of e
1, set function = L + or – e
2, theta = |x-c|
2.3
Limit theorems
Limit of product: Lim (f(x)
g(x)) as = lim f(x)
g(x) = AB
Limit of quotient: Lim (f(x) / g(x)) as = lim f(x) / g(x) = A/B B ≠0
Limit of difference: Lim (f(x) – g(x)) as = lim f(x)- g(x) = A-B
Lim of constant time function: lim k
f(x) = k
lim f(x) = KA
Limit of Sum: Lim (f(x) + g(x)) as = lim f(x)+ g(x) = A+B
Lim of Identity: lim X = C
Lim of a constant: lim K = K
2.6
Intermediate value theorem (IVT)
If a function is continuous for all x in the closed interval (a,b) and y is a number between f(a) and f(b) then there is a number x=c in (a,b) for which f(c) = y exactly
Ex: “f is a polynomial so f is continuous, direct substitution shows that f(3)=5 and f(5)=21, 12 is between 5 and 21 so the IVT applies, thus there exists a value of c between 3 and 5 such that f(c) = 12 exactly