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Problem 76

True or False? In Exercises $73-78$ , determine w…

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University of Delaware
Problem 75

True or False? In Exercises $73-78$ , determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.
If $p(x)$ is a polynomial function, then $p$ has exactly one antiderivative whose graph contains the origin.

Answer

True, explanation inside.

True or False? In Exercises $73-78$ , determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. Each antiderivative of an $n$ th-degree polynomial function is an $(n+1)$ th-degree polynomial function. True or False? In Exercises $73-78$ , determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. If $F(x)$ and $G(x)$ are antiderivatives of $f(x),$ then $$F(x)=G(x)+C$$ True or False? In Exercises $73-76$ , determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. If $$\lim _{x \rightarrow c} f(x)=L,$ then $f(c)=L$$ True or False? In Exercises $75-78$ , determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. If $b^{2}-4 a c=0$ and $a \neq 0,$ then the graph of $$y=a x^{2}+b x+c$$ has only one $x$ -intercept.
Chapter 4
Integration
Section 1
Antiderivatives and Indefinite Integration
Calculus of a Single Variable