Limit Process
Graphically
Analytically
Word Problems
100
The Limit Process
What is (f(x+Δx)-f(x))/(Δx)
100
lim x-> 2
What is 2
100
lim x->-3 (x^2+3x)
What is 0
100
A store is going out of business and is decreasing the price of their inventory by 50% ever day. What value will it approach?
What is $0
200
4x^2-2
What is 8x
200
lim x->1
What is ∞
200
lim x->7 (5x)/((x+2)^1/2)
What is 35/3
200
A man had $50 in his bank account. Every month the man gains 20% interest. What amount is he approaching?
What is ∞
300
lim Δx-> 0 ((x+Δx)^2-x^2)/(Δx)
What is 2x
300
lim x->-1
What is the Limit Does Not Exist
300
lim x->5 (x-5)/(x^2-25)
What is 1/10
300
A painter is working at 100 ft from the ground and drops his paint brush onto the street below. The function s(t)=-16^2+100 gives the height of the paintbrush as it falls to the ground. The velocity at time, t=2 sec, is given by lim t->2 (s(2)-s(t))/(2-t). Evaluate this limit to find the velocity of the paintbrush at 2 seconds.
What is -64 ft/sec
400
(2)/(x)
What is (-2)/(x^2)
400
lim x->2- (FROM THE LEFT)
What is 3
400
lim x->-3 (x)/((x^2-9)^1/2)
What is the Limit Does Not Exist
400
A boy is given $32 on his birthday by his father. Each day after receiving his original gift he receives half the amount of the day before. How much money will he have five days after his birthday?
What is $63
500
lim Δx-> 0 ((x+Δx)^2-2(x+Δx)+1-(x^2-2x+1))/(Δx)
What is 2x-1
500
lim x->-1
What is 2
500
lim x->4 ((x)^1/2-2)/(x-4)
What is 4
500
If this pattern continues, what will the triangle's area approach? (Darkened areas have been removed)
What is 0
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