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Question:
Please ensure that all working is shown and all steps are shown with instructions.
Limits & Continuity
Question 1: Find the limits of the following
(a) Limx→∞ (x5 - 5x3 + 6x2)/(2x6 + 6x4 + x3)
(b) Limx→0 (5x1/2 + 3x2/3 + 4x3/4)/(6x1/3 + 9x1/5)
Question 2:
The population of iguanas introduced into an isolated island is given by
P(t) = 72/(9-t), 0 ≤ t ≤ 9 where t is measured in months.
i. Find the number of iguanas present in the island intially.
ii. Show that the population of iguanas is increasing without bound.
Question 3:
a. Given f(x) = -1 if x < -2
x+1 if -2 ≤ x ≤ 1
x2 + x + 1 if x > 1
Is f(x) continuous
i. As x tends to -2?
ii. As x tends to 1?
iii. Everywhere throughout its domain?
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