. Let f(x) = 3x^2 + 5x. Using the limit definition of derivative
prove that f '(x) = 6x + 5
Then, Find the tangent line of f(x) at x = 3
Finally, Find the average rate of change between x = −1 and x =
2
a) State the definition that a function f(x) is continuous at x
= a. b) Let f(x) = ax^2 + b if 0 < x ≤ 2
18/x+1 if x > 2
If f(1) = 3, determine the values of a and b for which f(x) is
continuous for all x > 0.
a)
use the sequential definition of continuity to prove that f(x)=|x|
is continuous.
b) theorem 17.3 states that if f is continuous at x0, then |f|
is continuous at x0. is the converse true? if so, prove it. if not
find a counterexample.
hint: use counterexample
Two questions:
2) Use the limit definition of the derivative to find the
derivative of f(x)= x^3 - 9x
3) Using limits, find an equation of the line tangent to the
function of g(x)= 4/x^2 at x= -2
Show All Work please! thank you :)
Prove
1. Let f : A→ B and g : B → C . If g 。 f is one-to-one, then f
is one-to-one.
2. Equivalence of sets is an equivalence relation (you may use
other theorems without stating them for this one).