Free Printable Limits (An analytical approach)

1.

Polynomial function P(x)

$\lim_{x\rightarrow c}P\left(x\right)=P\left(c\right)$

(check the appropriate box)

a)

Always

b)

Sometimes

c)

Never

2.

Polynomial function P(x)

Graph of P(x)

(check all that apply)

a)

line

b)

half parabola

c)

parabola

d)

parts of parabolas

e)

hyperbola

3.

$\lim_{x\ \rightarrow\ 9}\ \left(4\ x^4-37\ x^3+12\ x^2-32\ x+38\right)=N$

Submit $N$

(a)

4.

Polynomial function P(x)

Point $\left[c,P\left(c\right)\right]$ lies on the graph of P(x)

ALGEBRA term: $word$ point

Submit $word$ (small letters)

(a)

5.

$\lim_{x\ \rightarrow\ 18}\sqrt{39\ x+82}\ =N$

Submit $N$

(a)

6.

A limit (if it exists) is a(n)

a)

x-value at a point

b)

y-value at a point

c)

point (x , y)

d)

indeterminable form

7.

L'Hopital's Rule can be utilized to evaluate the limit of a polynomial function as x approaches c.

a)

Always

b)

Sometimes

c)

Never

8.

Which limit(s) can be found by direct substitution?

(check all that apply)

a)

$\lim_{x\ \rightarrow\ 5}\left(4\ x+9\right)$

b)

$\lim_{x\ \rightarrow\ 12}\frac{x^{\ 2}-144}{x-12}$

c)

$\lim_{x\ \rightarrow\frac{\pi}{\ 3}}\cos\left(x\right)$

d)

$\lim_{x\ \rightarrow\ 7}\frac{\sqrt{x+18}-5}{x-7}$

9.

$\lim_{x\ \rightarrow\ \frac{5\ \pi}{4}}\ \left[\ \cot\left(x\right)\ \sin\left(x\right)\ \right]=N$

a)

$N=\frac{\sqrt{3}}{2}$

b)

$N=\frac{\sqrt{2}}{2}$

c)

$N=-\ \frac{\sqrt{3}}{2}$

d)

$N=-\ \frac{\sqrt{2}}{2}$

10.

Polynomial function P(x)

Point $\left[c,P\left(c\right)\right]$ lies on the graph of P(x)

CALCULUS term: point of $word$

Submit $word$ (small letters)

(a)

Limits (An analytical approach)

Total questions: 10

Worksheet time: 10mins

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