Question

Use the definition of continuity and the properties of limits to show that the function is continuous at teh given number a.

f(x) = (x+2x^3)^4 , a = -1

Answer 1

this one is much easier than the last one. property of the limit basically in this case means replace x by -1 and justify each step

Answer 2

\[\lim_{x\rightarrow -1}(x+2x^3)^4\]
\[=(\lim_{x\rightarrow -1}x+2\lim_{x\rightarrow -1}x^3)^4\] etc

Answer 3

use limit of power is power of limits, limit of sum is sum of limits and limit of product is product of limits

Answer 4

so how do we show taht is is continuos