Answer:
continuous.
Step-by-step explanation:
Given function is [tex]f(x)=5x^4-9x^3+x-7[/tex].
and value of a = 7.
Now we need to find if the given function [tex]f(x)=5x^4-9x^3+x-7[/tex] is continuous or not.
By definition of continuity, we know that a function is continuous at a given point if both left and right hand limits are equal.
Left Hand Limit = LHL
[tex]LHL=\lim_{x\rightarrow 7^-}f(x)=5(7)^4-9(7)^3+(7)-7=8918[/tex]
Right Hand Limit = RHL
[tex]RHL=\lim_{x\rightarrow 7^+}f(x)=5(7)^4-9(7)^3+(7)-7=8918[/tex]
Since both limits are equal at a=7 so we can say that given function is continuous at a=7
