I'll provide questions across various difficulty levels and include a mix of problem types like multiple
choice, short answer, and long problems. Let's start with some core topics like limits, derivatives,
integrals, and applications of differentiation and integration.
### **Calculus Test Bank**
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### **Topic 1: Limits and Continuity**
#### **Multiple Choice**
1. **Evaluate the limit:**
\[
\lim_{{x \to 2}} \frac{x^2 - 4}{x - 2}
\]
a) 2
b) 4
c) 0
d) 4x
2. **Determine the limit if it exists:**
\[
\lim_{{x \to \infty}} \frac{5x^2 + 3x + 1}{2x^2 + x - 1}
\]
a) \( \frac{5}{2} \)
b) 1
c) 0
d) Infinity
#### **Short Answer**
3. **Find the value of \(c\) such that the function \( f(x) = \begin{cases}
x^2 + c, & x \neq 3 \\
