Functions
What is the name for an input to a function?
Find the inputs for the following:
sqrt(3x+2)
Domain
x>=-2/3
Is
No
What is the derivative of:
x^2 + 10x -12
2x + 10
What is a cusp?
a point where the slopes on either side of the point are not the same
What is the limit (4x+2) as x approaches -3?
-10
The _____ is a method for checking if a graph is a function or not by ensuring every x value has only one y value
Vertical Line Test
What is the definition of removable discontinuity?
Limit as f approaches a exists
What is the derivative of:
f(x) = pi
0
Name two ways a function can be not differentiable
- cusp
- discontinuous
What is the limit of (2x^2-3x+1)/(5x+4) as x approaches 3?
10/19
Find the inverse of 3x-4
1/3x + 4/3
What is the definition of jump discontinuity?
Both limits exist, but they are not the same
What is the derivative of:
(12x^2) * (cosx)
24x*cosx - sinx*12x^2
What is the product rule?
(f(x)*g(x))' = f'(x)*g(x) + f(x)*g'(x)
What is the limit of (sqrt(x+2)-1)/(x+1)
1/2
What is the name of the outputs of a function?
Find the "outputs" of this function:
3/(x-2)
Range
all real numbers except y=0
What is the definition of infinite discontinuity?
(5x^2)/(4x + 3)
(20x^2+30x)/(4x+3)^2
What is the quotient rule?
(f(x)/g(x))' = [f'(x)*g(x) - f(x)*g'(x)]/g(x)^2
How do we know if a limit exists?
Limit as we approach the point from both directions exists and is the same value
Use exponent laws to simplify:
[(
x^8y^2
What are the three parts of the definition of continuity?
1 f(a) is defined
2 limit exists
3 limit = f(a)
What is the derivative of:
f(x)=(2x^3+2x-1)^4
4(2x^3+2x-1)^3 * (6x^2+2)
What is the Chain Rule?
(f(g(x)))' = f'(g(x))*g'(x)
What is the Squeeze Theorem?
f(x) <= g(x) <= h(x)
We use this generally to show that limits of f(x) and h(x) are the same at certain points