Find the limit if it exists. Justify your answer. Lim x tends to infinity [2x^2

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Find the limit if it exists. Justify your answer. Lim x tends to infinity [2x^2 + x - 1/x^2 - 3x] = Lim x tends to infinity [2 x/e^x] = Lim x tends to infinity [ln x/e^x] = Lim x tends to infinity [ln x/x] = Find the limit if it exists. Complete Solution is required. Lim x tends to infinity [x - 4/ root x - 2] Consider the function f(x) = x^1/3(8 - x). [f'(x) = ] Find the critical points of f(x) if any, x1 = & x2 = TRUE OR FALSE f(x) is increasing on the interval (0, 2). TRUE OR FALSE f(x) is increasing on the interval (2, infinity). TRUE OR FALSE f(x) is increasing on the interval (-infinity, 0).

Explanation / Answer

a) 2
b) 0
c) 0
d) 0

2) Limit does not exits as we have (x-4) (sqrt(x) +2)/(x-4)
=> sqrt(x) +2 which goes to infinity
3) a) x =2 is the critical point
b) True
c) False
d) True

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