Free Printable L'Hopital's Rule and Related Rates of Growth

1.

Find the limit of $\lim_{x\rightarrow0}\left(\frac{\sin5x}{\sin2x}\right).$

a)

2/5

b)

0

c)

$\infty$

d)

5/2

2.

Find the limit of $\lim_{x\rightarrow\infty}\left(\frac{\ln x}{x}\right).$

a)

$\infty$

b)

0

c)

1

d)

1/2

3.

Find the limit of $\lim_{x\rightarrow\infty}\left(\frac{2x^3+5x^2-7}{x^2-8x+5}\right).$

a)

2

b)

0

c)

$\infty$

d)

3

4.

Find the limit:

a)

0

b)

$\infty$

c)

1

d)

1/2

5.

Determine the convergence or divergence of the sequence. If it converges, find its limit.

$a_n=\frac{3n^2-1}{2n^2+1}$

a)

diverges

b)

converges to 0

c)

converges to 3/2

d)

cannot be determined

6.

Determine whether f grows faster than, slower than, or at the same rate as g as $x\rightarrow\infty.$
$f\left(x\right)=10x^3+2x^2,\ g\left(x\right)=e^x$

a)

f grows faster than g

b)

f grows slower than g

c)

f grows at the same rate as g

7.

Determine whether f grows faster than, slower than, or at the same rate as g as $x\rightarrow\infty.$
$f\left(x\right)=x,\ g\left(x\right)=5x$

a)

f grows faster than g

b)

f grows slower than g

c)

f grows at the same rate as g

8.

Determine whether f grows faster than, slower than, or at the same rate as g as $x\rightarrow\infty.$
$f\left(x\right)=x,\ g\left(x\right)=\tan^{-1}\left(x\right)$

a)

f grows faster than g

b)

f grows slower than g

c)

f grows at the same rate as g

9.

$\frac{d}{dx}\left(\frac{1}{2x}\right)=$

(a)

10.

$\int_{ }^{ }e^{5x}dx=$

(a)

L'Hopital's Rule and Related Rates of Growth

Total questions: 10

Worksheet time: 3hrs 30mins

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