Calculus 1 Exam

1.4

100

How do you find the equation of a line?

Y= mx+b

y-y₁=m(x-x₁)

200

Draw a tangent line

/o

300

How do you find average velocity?

y₂-y₁/x₂-x₁

400

Find the equations at the tangent line to the parabola y=x² at the point (1,1)

y=2x-1

500

Find the limit if it exists 

lim_x->0 1/x² =

infinity 

Random

100

suppose that limit f(x)=11 and lim g(x)=7. Find lim_x->5[2f(x)-g(x)]

15

200

lim_x-5 (x²-5x)/(x²-25)

1/2

300

Evaluate the limit and state any laws, properties, or theorems used.

lim_u->-2(9-u³+2u²)^1/2

5 

1) The limit can go inside the square root since it is positive and even

2) Constant Rule

3) Sum and Difference Rule

4) Direct substitution

400

Evaluate the limit

lim_x->24((x+1)^1/2-5)/(x-24)

1/10

500

Name as many limit laws as you can for 100 points each.

SUM LAW

DIFFERENCE LAW

CONSTANT MULTIPLE LAW

PRODUCT LAW

QUOTIENT LAW

POWER LAW

CONSTANT LAW

DIRECT SUBSTITUTION

DIRECT SUBSTITUTION WITH THE POWER LAW

LIMIT INSIDE THE SQUARE ROOT

1.6

100

Find the vertical asymptote(s) 

h(x)= x+2/ x²-1 

x=-1,1

200

Evaluate the limit 

lim_x->-2 (x³+2x²-1)/(5-3x)

-1/11

300

If 2x<₌g(x)<₌x⁴-x²+2 for all x then evaluate the lim_x->1

lim_x->1=2

400

Find lim_h->0= ((9+h)^1/2-3)/ h

1/6

500

lim_x->0 sin(7x)/4x

7/4

1.7

100

if you have to values of delta which one do you chose as a value?

the smallest one

200

how do you find epsilon

by finding the difference between y values

300

Use the given graph of f to find a number delta such that if l x-1 l < delta then l f(x)-1 l <0.2

.1

1.8

100

What makes a limit function discontinuous?

if there is a hole/break

infinite discontinuity

Jump discontinuity

200

What 3 things are required for limit function to be continuous

lim_x->a f(x)= f(a)

f(a) is defined (meaning it is in the domain of f(x))

lim_x->a f(x) exists 

lim_x->a f(x)= f(a) (meaning it is true)

300

State each x-value where f is not continuous. 

x= -2

x= -1

x= 0

x= 1

400

which of the following limits do not exist? (graph #2)

a) lim_x->-2 f(x)

b) lim_x->0 f(x)

c) lim_x->1 f(x)

d) lim_x->2f(x)

b) lim_x->0 f(x)

c) lim_x->1 f(x)