Calculating limits using algebra

Practice Questions

AP Calculus AB › Calculating limits using algebra

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1

Define $f (x) = \begin{Bmatrix} x^{2}+2x+ 3& x< 0 \ a \cos\theta x & x \ge 0 \end{matrix}$ for some real $a,\theta$ .

Evaluate and $\theta$ so that is both continuous and differentiable at .

2

Evaluate the following limit:

$\lim_{x\rightarrow 4}\frac{x^{2}+2x-24}{x-4}$

3

$f(x) = \left{\begin{matrix} \frac{2}{x+2}&x<0 \ 0 &x= 0 \ 2x+1 & x > 0 \end{matrix}\right.$

Which of the following is equal to $\lim_{x\rightarrow 0 }f(x)$ ?

4

Evaluate the following limit:

$\lim_{x\rightarrow 0}\frac{x^3+5x^2+8x}{x}$

5

Calculate $\lim_{x\rightarrow 5} \frac{x^2-25}{x-5}$

6

$\lim_{x\rightarrow 2}\frac{x^2+5x-14}{x-2}=?$

7

Find the limit:

$\lim_{x\rightarrow \propto }\frac{4x^3+3x^2+10}{10x^3+x^2+8x}$

8

$\lim_{x\rightarrow -3}\frac{2x+4}{x-3}=?$

9

$\begin{align*}&\text{Find the limit of }f(x)=\frac{4x^{2} - 68x - 152}{2x^{2} - 62x + 456}\&\text{At the location }x=19\end{align*}$

10

$\begin{align*}&\text{Find the limit of }f(x)=\frac{5x^{2} - 41x - 36}{x^{2} - 21x + 108}\&\text{At the location }x=9\end{align*}$

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