Limits
More Limits
Continuity
Limits Involving Infinity
Derivatives
100
lim x->1 (x²-1)/(x-1)
What is 2
100
lim x->0 [(3+h)²-9]/h
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
Find the limit: lim x-> -3+ (x + 2) / (x + 3)
What is -∞
100
f'(3)= lim h->0 [(3 + h)² -3²] / h
What is 6
200
lim x->4 1/(X-4)
What is DNE
200
lim x->2 (x² + x - 6) / (x-2)
What is 5
200
Given the function, f(x)= (2x² + 9x - 5) / [(x + 5)(x - 1)]
What is removable at x=-5, and infinite at x=1
200
lim x-> 1 (2 - x) / (x - 1)²
What is ∞
200
f(x)= 4x² Find f'(3)
What is 24
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-a, 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->3+ ln(x² - 9)
What is -∞
300
f(x)= x²-4x Find f'(2)
What is 0
400
lim -> -2 (x+2) / (x³ + 8)
What is 1/12
400
lim x-> 7 {[(x + 2)^1/2] -3} / (x-7)
What is 1/6
400
Given the function f(x)=(e^x) - 2, show that f(x) will have a root on the interval [0,3]
What is f(x) is an exponential function continuous at all reals, therefore continuous at [0,3]
400
lim x->∞ (x³ + 5x) / (2x³ - x² + 4)
What is 1/2
400
f(x)=x²-3 Find f'(x)
What is 2x
500
lim t->0 [(t²+9)^1/2] -3
What is 1/6
500
lim x-> -4 [(1/4) + (1/x)] / (4 + x)
What is -1/16
500
Given the function f(x) = ln(5x +1) prove that the function is continuous on the interval [1,2]
What is ln(5x +1) is a log function, therefore continuous on its domain, x(-1/6, ∞)
500
u->∞ (4u⁴ + 5) / (u² - 2) (2u² - 1)
What is 2
500
y= 3x² + 3x + 3
What is 6x + 3
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