Limits & Continuity
The value of the limit x-->3 of (2x+1)?
What is: 7
The limit as x-->-1 of (3x2-2x+5)
What is: 10
The derivative of a function at a point gives the slope of this line
What is: Tangent Line
If c(x) is the price of potatoes then c'(x) represents
What is: The rate of change of the price of potatoes
This type of limit considers x approaching a only from values less than a.
What is: Left-hand limit
The limit as x-->2 of [(x2-4)/(x-2)]
4
Using the limit definition of a derivative find f'(1) for f(x)=x2
What is: 2
A ball is thrown upward: It's position is given by the equation h(t)=40t−16t2 . t is seconds since thrown
The velocity at t=1 second
What is: 8ft/second
The limit as x-->0 of Sin(3x)/x
What is: 3
s(t)=t2−4t is position (meters), the velocity at t=3 seconds
What is: 2meters/second
If f(x) is differentiable at x=a , then f must be ___ at a
What is: Continuous
The three conditions required for a function ff to be continuous at x=ax=a.
What is: 1. f(a) defined 2. limit as x-->a of f(x) exists 3. limit as x-->a of f(x) = f(a)
The limit as x-->Infinity of (2x2-3x+1)/(5x2+4x-7)
What is: 2/5
Graph:https://www.desmos.com/calculator/glvvlrtdxx
The derivative of the graph at x=3
What is: DNE
f(x)={cx+2, x≤1
{x2+3, x>1
What value of C makes the piece wise function continuous at x=1
The limit as x-->0 of x2 Sin(1/x)
https://www.desmos.com/calculator/owvhsjho82
Using the table, estimate the value f'(0) to 2 decimal places
What is: 0.69
A ball is thrown upward: It's position is given by the equation h(t)=40t−16t2 . t is seconds since thrown
The ball reaches it's max height at
What is: 1.25 seconds