Calculus

One or more correct

• AThe value of $I(a)$ is independent of the value of $a$
• BThe value of $I(a)$ can vary with the value of $a$
• CThere exists $a \in (-\infty, +\infty)$ such that $I(a)$ is a positive real number
• DThere exists $a \in (-\infty, +\infty)$ such that $I(a)$ is a negative real number

Numerical answer

Single correct

• A$\sqrt{e}$
• B$e$
• C$e^2$
• D$e - 1$

Single correct

• A0
• B1
• C2
• D$-1$

Numerical answer

Answer key coming soon

Single correct

• A$\dfrac{2}{\pi}$ and $\dfrac{16}{\pi}$
• B$\dfrac{2}{\pi}$ and 0
• C$\dfrac{4}{\pi}$ and 0
• D$\dfrac{4}{\pi}$ and $\dfrac{16}{\pi}$

Answer key coming soon

Numerical answer

Answer key coming soon

Single correct

• AII only
• BIII only
• CII and III only
• DI, II and III

Single correct

• A$f(0)f(4) < 0$
• B$f(0)f(4) > 0$
• C$f(0) + f(4) > 0$
• D$f(0) + f(4) < 0$

Single correct

• AOnly I
• BOnly II
• CBoth I and II
• DNeither I nor II