Limits
More Limits
Continuity
Limits Involving Infinity
Miscellaneous
100
lim x->1 (x²-1)/(x-1)
What is 2
100
lim_(x->0)[(3+x)²-9]/x
What is 6
100
Given the function f(x)= (2x² + 9x - 5) / [(x +5) (x - 1)] find the discontinuity and label as a removable, jump, or infintie discontinuity.
What is removable at x= -5, and infinite at x= 1
100
lim_(x->-3^+)(x+2)/(x+3)
Describe the end-behavior and the limit
What is -∞ and DNE
100
Use the Intermediate Value Theorem to show that
f(x)=x^3+2x-1
has a zero on the interval [-1,1]
a) f(x) is continuous on the interval [-1,1]
b) f(-1)=-4 f(1)=2
c) By IVT, there exists an x value, c on the interval [-1,1] where f(c)=0
200
lim_(x->9)f(x)=7 and lim_(x->9)g(x)=2 Solve lim_(x->9){f(x)+g(x)}
What 9
200
lim_(x->2)(x² + x - 6) / (x-2)
What is 5
200
Given the function, f(x)=(-5x-15)/(2x^2-18 , find all holes and vertical asymptotes. What kind of discontinuities would these be?
What is a hole at x=-3 (removable), and a vertical asymptote at x=3 (infinite)
200
lim_(x-> 3) (x^2-3x+2) / (x^2-5x+6)
What is -∞ and DNE?
200
lim_(x->1^-)|x-1|/(x-1)
What is -1
300
lim_(t -> -3) (t² - 9) / (2t² + 7t +3)
What is
6/5
300
lim_(h-> 0)[(4+h)² - 16] / h
What is 8
300
Given the function, f(x) = {(x²-9, x≠3), (7, x=3) :} find any points of discontinuity and label as a removable, jump, infinite, or oscillating discontinuity.
What is removable at x=3
300
lim_(x->oo)(3x-1)/(4x^2+x)
What is 0
300
At what values of x is f continuous?
(-oo,1)uu(1,2)uu(2,oo)
400
lim_(x->0)sin(5x)/(8x)
What is
5/8
400
lim_(x->7) (sqrt(x + 2) -3) / (x-7)
What is 1/6
400
Using limits, define k so that f(x) = {(x²-16, x≠3), (k, x=3) :} is continuous at x=3
f(3)=-7
lim_(x->3)f(x)=lim_(x->3)(x^2-16)=3^2-16=-7
400
lim_ (x->∞) (x³ + 5x) / (2x³ - x² + 4)
What is 1/2
400
Find all horizontal asymptotes for the function h(x) that is written on the white board.
What is y = 2 and y = -2
500
What is
8
500
lim_(x-> -4) [1/4 + 1/x] / (4 + x)
What is -1/16
500
This value assigned to b will make the function g(x)={(x^3, x<1/2),(bx^2, x>=1/2):} continuous as x=1/2
What is
b=1/2
500
lim_(x->∞) (4u⁴ + 5) / [(u² - 2) (2u² - 1)]
What is 2
500
Use the IVT to find the value of c for f(x)=3x^2+x+4 on the interval [-2,0] where f(c)=6 . Find c
c=-1