Limits and Derivatives

Topics in this chapter

• Evaluating Algebraic and Trigonometric Limits
• Continuity of Piecewise and Special Functions
• Derivatives From First Principles
• Differentiation Rules and Standard Functions
• Tangents and Stationary Points

Cheat sheet

Practice questions

1. Question 1Q-C03C13

   Evaluate the limit: $\lim_{x\to 2}\frac{x^2-4}{x-2}$.

   1. A.2
   2. B.4
   3. C.6
   4. D.Does not exist
   See the answer and solution
2. Question 2Q-B79CB5

   Evaluate $\lim_{x\to 0}\frac{\sqrt{1+2x}-\sqrt{1-2x}}{x}$.

   1. A.0
   2. B.1
   3. C.2
   4. D.4
   See the answer and solution
3. Question 3Q-955CAE

   If $y=(x^2+1)(x^3-2)$, find $\frac{dy}{dx}$ at $x=1$.

   1. A.2
   2. B.3
   3. C.4
   4. D.6
   See the answer and solution
4. Question 4Q-457DDA

   Using the definition of derivative, find the derivative of $f(x)=\frac{1}{x}$ at $x=2$.

   See the answer and solution
5. Question 5Q-F42D00

   Evaluate limₓ→0 (1 − cos 2x)/x².

   1. A.0
   2. B.1
   3. C.2
   4. D.4
   See the answer and solution