5.1 Limits and the derivative Quiz

1. A function has $g(3.9)=7.8$, $g(3.99)=7.98$, $g(3.999)=7.998$ and $g(4.1)=8.2$, $g(4.01)=8.02$, $g(4.001)=8.002$. Estimate $\lim_{x\to4}g(x)$.

• A. $7.998$
• B. $8$
• C. $8.002$
• D. $4$

2. What does $\frac{ds}{dt}$ represent?

• A. The distance $s$ at time $t$
• B. The area under the graph of $s$
• C. The average of $s$ and $t$
• D. The rate of change of $s$ with respect to $t$

3. For $f(x)=x^2$, find the gradient of the chord from $x=2$ to $x=2.1$.

• A. $4.1$
• B. $4.41$
• C. $0.41$
• D. $4$

4. $V$ is in litres and $t$ in minutes. What are the units of $\frac{dV}{dt}$?

• A. Litres
• B. Minutes
• C. Litres per minute
• D. Minutes per litre

5. $f'(3)=-2$. What does this say about the graph of $y=f(x)$ at $x=3$?

• A. The curve has a value of $-2$
• B. The tangent has gradient $-2$, so the curve is falling
• C. The tangent has gradient $2$
• D. The curve is rising