Free Printable Unit Zero Review

1.

What is the answer when $\frac{1}{0}$ ?

a)

1

b)

0

c)

$\pm\infty$

d)

Need to do more work!

2.

Which of the following is not an indeterminate form?

a)

$0^{\infty}$

b)

$\infty-\infty$

c)

$\frac{\infty}{\infty}$

d)

$0\times\infty$

3.

What is the answer when $\infty^0$ ?

a)

1

b)

0

c)

$\infty$

d)

Need to do more work!

4.

$\lim_{x\rightarrow\infty}\ e^{-x}\sqrt[]{x}$

a)

INDETERMINATE

b)

NOT INDETERMINATE

5.

$\lim_{x\rightarrow\infty}\left(1+\frac{1}{x}\right)^x$

a)

INDETERMINATE

b)

NOT INDETERMINATE

6.

$\lim_{x\rightarrow\infty}\left(\frac{1}{x}\right)^x$

a)

INDETERMINATE

b)

NOT INDETERMINATE

7.

$\lim_{x\rightarrow\infty}\left(e^{-x}\right)^x$

a)

INDETERMINATE

b)

NOT INDETERMINATE

8.

4 lines

9.

$\lim_{x\rightarrow\left(\frac{\pi}{2}\right)}\left(\tan x\cdot\ln\left(\sin x\right)\right)$

a)

INDETERMINATE

b)

NOT INDETERMINATE

10.

Solve with euler's method

a)

A

b)

B

c)

C

d)

D

e)

E

11.

Solve with euler's method

a)

A

b)

B

c)

C

d)

D

12.

Double Points

let y=f(x) be the solution to the differential equation dy/dx = 2x+y. Let f(0) =k. Where k is a constant. Euler's method, starting at x=0 with steps of size 0.5 gives the approximation of f(1)=3.5. What is the value of k

(a)

13.

What is the answer to Problem 4? (Calculator Active)

a)

A

b)

B

c)

C

d)

D

e)

E

14.

Triple Points

a)

A

b)

B

c)

C

d)

D

15.

Given the logistic equation for the growth of a population of creatures, P, find the following.

a)

A)

b)

B)

c)

C)

d)

D)

16.

Given the logistic equation for the growth of a population of creatures, P, find the following.

a)

A)

b)

B)

c)

C)

d)

D)

17.

Given the logistic equation for the growth of a population of creatures, P, find the following.

a)

A)

b)

B)

c)

C)

d)

D)

18.

Given the logistic equation for the growth of a population of creatures, P, find the following.

a)

A)

b)

B)

c)

C)

d)

D)

19.

Given the logistic equation for the growth of a population of creatures, P, find the following.

a)

A)

b)

B)

c)

C)

d)

D)

20.

Solve

a)

A

b)

B

c)

C

d)

D

21.

Given the logistic equation for the growth of a population of creatures, P, find the following.

a)

A)

b)

B)

c)

C)

d)

D)

22.

a)

A

b)

B

c)

C

d)

D

e)

E

23.

Double pts

a)

A

b)

B

c)

C

d)

D

e)

E

24.

Double points

a)

A

b)

B

c)

C

d)

D

e)

E

25.

Double Points

a)

A

b)

B

c)

C

d)

D

e)

E

26.

a)

A

b)

B

c)

C

d)

D

27.

a)

A

b)

B

c)

C

d)

D

28.

a)

A

b)

B

c)

C

d)

D

29.

Which of the following expressions give the lenght of the graph of $x=y^3$ for $-2\le y\le2.$

a)

$\int_{-2}^2\left(1+y^6\right)dy$

b)

$\int_{-2}^2\left(1+y^6\right)^{.5}dy$

c)

$\int_{-2}^2\left(1+9y^4\right)dy$

d)

$\int_{-2}^2\left(1+9y^4\right)^{.5}dy$

30.

Find the length of the curve described by $y=\frac{2}{3}x^{\frac{3}{2}}$ for $0\le x\le8.$

a)

$\frac{26}{3}$

b)

$\frac{52}{3}$

c)

$\frac{512\sqrt{2}}{15}$

d)

96

31.

a)

A

b)

B

c)

C

d)

D

e)

E

32.

Which of the following expressions should be used to find the length of the curve $y=x^{\frac{2}{3}}$ for $-1\le x\le1$ .

a)

$2\int_0^1\sqrt{1+\frac{9}{4}y}dy$

b)

$\int_{-1}^1\sqrt{1+\frac{9}{4}y}dy$

c)

$\int_0^1\sqrt{1+y^3}dy$

d)

$2\int_0^1\sqrt{1+y^6}dy$

33.

$f\left(x\right)=\frac{x-1}{4x^2+1},\ -\frac{1}{2}\le x\le1$ What is the length of the smooth curve

a)

1.1089

b)

2.1089

c)

3.1089

d)

4.1089

34.

a)

A

b)

B

c)

C

d)

D

e)

E

35.

Factor and simplify to find the limit.

a)

0

b)

0.5

c)

2

d)

DNE

36.

Which mathematician is credited with actually discovering L'Hôpital's Rule?

a)

Guillaume de l'Hôpital

b)

Johann Bernoulli

c)

Isaac Newton

d)

Gottfried Leibniz

37.

a)

A

b)

B

c)

C

d)

D

38.

a)

A

b)

B

c)

C

d)

D

39.

a)

A

b)

B

c)

C

d)

D

40.

What is the general solution to the differential equation $\frac{dy}{dx}=\frac{\left(x-1\right)}{3y^2}$ for $y>0$ ?

a)

$y=\frac{1}{-\frac{3}{2}x^2+3x+C}$

b)

$y=\left(e^{\left(\frac{3x^2}{2}-3x+C\right)}\right)^{\frac{1}{2}}$

c)

$y=\left(x^2-x\right)^{\frac{1}{3}}+C$

d)

$y=\left(\frac{x^2}{2}-x+C\right)^{\frac{1}{3}}$

41.

Which of the following differential equations is not logistic?

a)

$\frac{dP}{dt}=P-P^2$

b)

$\frac{dy}{dt}=0.01y\left(100-y\right)$

c)

$\frac{dx}{dt}=0.8x-0.004x^2$

d)

$\frac{dR}{dt}=0.16\left(350-R\right)$

42.

Suppose P(t) is the particular solution of the differential equation $\frac{dP}{dt}=0.3P\left(50-P\right)$ with the initial condition if t=0, then P=5. Then $\lim_{t\rightarrow\infty}P\left(t\right)$ equals

a)

$\infty$

b)

0.3

c)

15

d)

50

43.

A population grows according to the logistic differential equation $\frac{dP}{dt}=0.01P\left(3-\frac{p}{2000}\right)$ . According to the model the carrying capacity is

a)

2000

b)

4000

c)

6000

d)

10,000

44.

A population P grows according ot the logistic differential equation $\frac{dP}{dt}=0.08P\left(1-\frac{P}{2000}\right)$ , where t is measured in years. What is the population when it is increasing most rapidly?

a)

40

b)

80

c)

1000

d)

2000

45.

A virus spreads among a population of N people at a rate proportional to the product of the number of people infected with the virus and the number of people not infected with the virus. Which differential equation can be used to model the situation with respect to t? Assume k is positive.

a)

$\frac{dP}{dt}=kP$

b)

$\frac{dP}{dt}=kN\left(N-P\right)$

c)

$\frac{dP}{dt}=kP\left(P-N\right)$

d)

$\frac{dP}{dt}=kP\left(N-P\right)$

Unit Zero Review

Total questions: 45

Worksheet time: 2hrs 39mins

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