How do you prove that the function #f(x) = (x + 2x^3)^4# is continuous at x=-1?

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How do you prove that the function #f(x) = (x + 2x^3)^4# is continuous at x=-1?

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Answer 1 · 2016-03-10T20:08:59

Since #f(-1) = lim x->-1 (f(x))# therefore f(x) is continuous at x = -1

Explanation:

#1. f(-1)=(-1+2(-1)^3)^4 =(-1-2)^4=(-3)^4=81#
#2. lim x->-1 [(x+2x^3)^4]->(-1+2(-1)^3)^4 =(-1-2)^4=(-3)^4=81#
#3.# Since #f(-1)# = #lim x->-1 f(x)# therefore f(x) is continuous at x = -1

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How do you prove that the function #f(x) = (x + 2x^3)^4# is continuous at x=-1?

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