Feedback wrapped around an NPN

Exercise 6.6 Feedback wrapped around an NPN - limiting factors

In the circuit below, the opamp is ideal ( $r_{i n} \to \infty, r_{o u t} = 0, a_{V} \to \infty)$ . For the BJT, you may assume that $i_{C} = I_{C 0} \cdot e^{}$

q $\cdot v_{B E} k T$ , with a finite $β f e$ .

pict

a): Draw a large signal graph of $v_{O U T}$ as a function of $v_{I N}$ .
b): Describe the range of $v_{O U T}$ for which the specified BJT element equation(s) hold.
c): What happens to $v_{X}$ for values of $v_{I N}$ very close to ground?

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