8. Differentiation
Interactive practice questions
Consider the function $f\left(x\right)=5x^2+1$f(x)=5x2+1.
a
Complete the table to find the exact values of $f\left(x\right)$f(x) as $x$x gets closer and closer to $2$2 from the left, and closer and closer to $2$2 from the right.
| $x$x | $1.9$1.9 | $1.99$1.99 | $1.999$1.999 | $2.001$2.001 | $2.01$2.01 | $2.1$2.1 |
|---|---|---|---|---|---|---|
| $f\left(x\right)$f(x) | $\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ |
b
Hence, find the value of $\lim_{x\to2}\left(5x^2+1\right)$limx→2(5x2+1).
Easy
3min
$\lim_{x\to-5}\left(\frac{x^2+4}{x+5}\right)$limx→−5(x2+4x+5)
Easy
< 1min
Consider the function $f\left(x\right)=\frac{2-x}{x^2+2}$f(x)=2−xx2+2.
Easy
5min
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