Introduction to Calculus

Question 1

What is Calculus?

Accepted Answer

All the above

Question 2

This is the main form of the Power Rule

Accepted Answer

if f(x)= xn, then f'(x)= nxn-1

Question 3

This is the equation for the slope of a tangent line

Accepted Answer

m=f'(x) for a given x

Question 4

Time in which Newton and Leibniz developed their Calculus foundations.

Accepted Answer

Mid-17th Century

Question 5

This is the Integral Symbol

Accepted Answer

∫

Question 6

What is a limit?

Accepted Answer

A value that a function approaches, but never reaches it.

Question 7

This is the formula that is used to determine the equation of a tangent line

Accepted Answer

y - y1 = m( x - x1)

Question 8

The basic rule of derivatives for a constant says...

Accepted Answer

if f(x) = a constant, its derivative is 0

Question 9

How do you represent derivatives?

Accepted Answer

d/dx or sin(x)'

Question 10

Solve for the antiderivative of 5x3

Accepted Answer

1.25x4 + C

Question 11

How do we calculate the Velocity by using derivatives?

Accepted Answer

With the derivative of the function of Position S'(t)

Question 12

What are Antiderivatives?

Accepted Answer

Antiderivatives are the inverse operations of derivatives, Antiderivatives are the backward operations of derivatives

Question 13

Modern calculus discoveries are often attributed to these two men.

Accepted Answer

Isaac Newton and Gottfried Leibniz

Question 14

The slope of a line like 2x is...

Accepted Answer

2

Question 15

Characteristic of tangent and normal lines

Accepted Answer

The product of their slopes is always -1

Question 16

Third derivative of 3x5

Accepted Answer

180x2

Question 17

Why do we add a C when solving Antiderivatives?

Accepted Answer

To represent that the antiderivative may have a constant

Question 18

First calculations found in 1280 BC are from the...

Accepted Answer

Egyptian Papyrus

Question 19

How do you calculate derivatives?

Accepted Answer

By calculating the slope of a function.

Question 20

Determine the slope of the tangent line of f(x)= x4-4x, in p(5,3)

Accepted Answer

496

Question 21

% is an ______ function

Accepted Answer

Undefined

Question 22

Limit of x approaching 4 is written as...

Accepted Answer

Lim x→4

Question 23

This volume wasn't integrated by Archimedes.

Accepted Answer

Prisms

Question 24

What is the contact point?

Accepted Answer

The point where a tangent touches a curve

Question 25

Method used by Archimedes to find an approximation to a circle's area...

Accepted Answer

Exhaustion

Question 26

What is a Derivative?

Accepted Answer

The slope of a function at any point.

Question 27

f(x)= 4x-5 is the same as...

Accepted Answer

y= 4x-5

Question 28

Characteristic of the tangent and normal lines

Accepted Answer

Both share the same contact point

Question 29

How do we represent an undefined function in a graph.

Accepted Answer

With a gap in the graph

Question 30

Which constant value did the method of exhaustion approximated?

Accepted Answer

π

Question 31

How do you determine the contact point of a function?

Accepted Answer

With f(x1)

Question 32

determine the slope of the normal line of f(x)= x4+5x when (5,3)

Accepted Answer

-.001

Question 33

What is the normal line?

Accepted Answer

Perpendicular line to the tangent of a curve in (x,y)

Question 34

This is a derivative rule.

Accepted Answer

The slope of a constant value is always 0

Question 35

What is a tangent line?

Accepted Answer

The straight line that touches a curve at one point

Question 36

This is the equation of the slope of the normal line

Accepted Answer

m= 1/f'(x)

Question 37

This is another form to name Integrals

Accepted Answer

Antiderivatives

Question 38

0/18 equals

Accepted Answer

0

Question 39

Solve for the Antiderivative of 2x

Accepted Answer

x2+C

Introduction to Calculus

Questions 39

Introduction to Calculus

Questions 39