<< Chapter < Page Chapter >> Page >

f ( x ) = e x + 2

An image of a graph. The x axis runs from -5 to 5 and the y axis runs from -5 to 5. The graph is of a curved increasing function that starts slightly above the line “y = 2” and begins increasing rapidly. There is no x intercept and the y intercept is at the point (0, 3).

Domain: all real numbers, range: ( 2 , ) , y = 2

Got questions? Get instant answers now!

f ( x ) = 3 x + 1

An image of a graph. The x axis runs from -5 to 5 and the y axis runs from -5 to 5. The graph is of a curved increasing function that starts slightly above the x axis and begins increasing rapidly. There is no x intercept and the y intercept is at the point (0, 3). Another point of the graph is at (-1, 1).

Domain: all real numbers, range: ( 0 , ) , y = 0

Got questions? Get instant answers now!

f ( x ) = 1 2 x

An image of a graph. The x axis runs from -5 to 5 and the y axis runs from -5 to 5. The graph is of a curved increasing function that increases until it comes close the line “y = 1” without touching it. There x intercept and the y intercept are both at the origin. Another point of the graph is at (-1, -1).

Domain: all real numbers, range: ( , 1 ) , y = 1

Got questions? Get instant answers now!

f ( x ) = e x 1

An image of a graph. The x axis runs from -5 to 5 and the y axis runs from -5 to 5. The graph is of a curved decreasing function that decreases until it comes close the line “y = -1” without touching it. There x intercept and the y intercept are both at the origin. There is an approximate point on the graph at (-1, 1.7).

Domain: all real numbers, range: ( −1 , ) , y = −1

Got questions? Get instant answers now!

For the following exercises, write the equation in equivalent exponential form.

log 8 2 = 1 3

8 1 / 3 = 2

Got questions? Get instant answers now!

ln ( 1 e 3 ) = −3

e −3 = 1 e 3

Got questions? Get instant answers now!

For the following exercises, write the equation in equivalent logarithmic form.

4 −2 = 1 16

log 4 ( 1 16 ) = −2

Got questions? Get instant answers now!

4 −3 / 2 = 0.125

log 4 0.125 = 3 2

Got questions? Get instant answers now!

For the following exercises, sketch the graph of the logarithmic function. Determine the domain, range, and vertical asymptote.

f ( x ) = ln ( x 1 )

An image of a graph. The x axis runs from -5 to 5 and the y axis runs from -5 to 5. The graph is of an increasing curved function which starts slightly to the right of the vertical line “x = 1”. There is no y intercept and the x intercept is at the approximate point (2, 0).

Domain: ( 1 , ) , range: ( , ) , x = 1

Got questions? Get instant answers now!

f ( x ) = 1 ln x

An image of a graph. The x axis runs from -1 to 9 and the y axis runs from -5 to 5. The graph is of a decreasing curved function which starts slightly to the right of the y axis. There is no y intercept and the x intercept is at the point (e, 0).

Domain: ( 0 , ) , range: ( , ) , x = 0

Got questions? Get instant answers now!

f ( x ) = ln ( x + 1 )

An image of a graph. The x axis runs from -5 to 5 and the y axis runs from -5 to 5. The graph is of an increasing curved function which starts slightly to the right of the vertical line “x = -1”. There y intercept and the x intercept are both at the origin.

Domain: ( −1 , ) , range: ( , ) , x = −1

Got questions? Get instant answers now!

For the following exercises, use properties of logarithms to write the expressions as a sum, difference, and/or product of logarithms.

log 3 9 a 3 b

2 + 3 log 3 a log 3 b

Got questions? Get instant answers now!

log 5 125 x y 3

3 2 + 1 2 log 5 x + 3 2 log 5 y

Got questions? Get instant answers now!

ln ( 6 e 3 )

3 2 + ln 6

Got questions? Get instant answers now!

For the following exercises, solve the exponential equation exactly.

e 3 x 15 = 0

ln 15 3

Got questions? Get instant answers now!

7 3 x 2 = 11

2 3 + log 11 3 log 7

Got questions? Get instant answers now!

For the following exercises, solve the logarithmic equation exactly, if possible.

log ( 2 x 7 ) = 0

x = 4

Got questions? Get instant answers now!

log 6 ( x + 9 ) + log 6 x = 2

x = 3

Got questions? Get instant answers now!

log 4 ( x + 2 ) log 4 ( x 1 ) = 0

Got questions? Get instant answers now!

ln x + ln ( x 2 ) = ln 4

1 + 5

Got questions? Get instant answers now!

For the following exercises, use the change-of-base formula and either base 10 or base e to evaluate the given expressions. Answer in exact form and in approximate form, rounding to four decimal places.

log 7 82

( log 82 log 7 2.2646 )

Got questions? Get instant answers now!

log 0.5 211

( log 211 log 0.5 7.7211 )

Got questions? Get instant answers now!

log 0.2 0.452

( log 0.452 log 0.2 0.4934 )

Got questions? Get instant answers now!

Rewrite the following expressions in terms of exponentials and simplify.

a. 2 cosh ( ln x ) b. cosh 4 x + sinh 4 x c. cosh 2 x sinh 2 x d. ln ( cosh x + sinh x ) + ln ( cosh x sinh x )

Got questions? Get instant answers now!

[T] The number of bacteria N in a culture after t days can be modeled by the function N ( t ) = 1300 · ( 2 ) t / 4 . Find the number of bacteria present after 15 days.

~ 17 , 491

Got questions? Get instant answers now!

[T] The demand D (in millions of barrels) for oil in an oil-rich country is given by the function D ( p ) = 150 · ( 2.7 ) −0.25 p , where p is the price (in dollars) of a barrel of oil. Find the amount of oil demanded (to the nearest million barrels) when the price is between $15 and $20.

Got questions? Get instant answers now!

[T] The amount A of a $100,000 investment paying continuously and compounded for t years is given by A ( t ) = 100,000 · e 0.055 t . Find the amount A accumulated in 5 years.

Approximately $131,653 is accumulated in 5 years.

Got questions? Get instant answers now!

[T] An investment is compounded monthly, quarterly, or yearly and is given by the function A = P ( 1 + j n ) n t , where A is the value of the investment at time t , P is the initial principle that was invested, j is the annual interest rate, and n is the number of time the interest is compounded per year. Given a yearly interest rate of 3.5% and an initial principle of $100,000, find the amount A accumulated in 5 years for interest that is compounded a. daily, b., monthly, c. quarterly, and d. yearly.

Got questions? Get instant answers now!

Questions & Answers

f(x) = x-2 g(x) = 3x + 5 fog(x)? f(x)/g(x)
Naufal Reply
fog(x)= f(g(x)) = x-2 = 3x+5-2 = 3x+3 f(x)/g(x)= x-2/3x+5
diron
pweding paturo nsa calculus?
jimmy
how to use fundamental theorem to solve exponential
JULIA Reply
find the bounded area of the parabola y^2=4x and y=16x
Omar Reply
what is absolute value means?
Geo Reply
Chicken nuggets
Hugh
🐔
MM
🐔🦃 nuggets
MM
(mathematics) For a complex number a+bi, the principal square root of the sum of the squares of its real and imaginary parts, √a2+b2 . Denoted by | |. The absolute value |x| of a real number x is √x2 , which is equal to x if x is non-negative, and −x if x is negative.
Ismael
find integration of loge x
Game Reply
find the volume of a solid about the y-axis, x=0, x=1, y=0, y=7+x^3
Godwin Reply
how does this work
Brad Reply
Can calculus give the answers as same as other methods give in basic classes while solving the numericals?
Cosmos Reply
log tan (x/4+x/2)
Rohan
please answer
Rohan
y=(x^2 + 3x).(eipix)
Claudia
is this a answer
Ismael
A Function F(X)=Sinx+cosx is odd or even?
WIZARD Reply
neither
David
Neither
Lovuyiso
f(x)=1/1+x^2 |=[-3,1]
Yuliana Reply
apa itu?
fauzi
determine the area of the region enclosed by x²+y=1,2x-y+4=0
Gerald Reply
Hi
MP
Hi too
Vic
hello please anyone with calculus PDF should share
Adegoke
Which kind of pdf do you want bro?
Aftab
hi
Abdul
can I get calculus in pdf
Abdul
explain for me
Usman
How to use it to slove fraction
Tricia Reply
Hello please can someone tell me the meaning of this group all about, yes I know is calculus group but yet nothing is showing up
Shodipo
You have downloaded the aplication Calculus Volume 1, tackling about lessons for (mostly) college freshmen, Calculus 1: Differential, and this group I think aims to let concerns and questions from students who want to clarify something about the subject. Well, this is what I guess so.
Jean
Im not in college but this will still help
nothing
how en where can u apply it
Migos
how can we scatch a parabola graph
Dever Reply
Ok
Endalkachew
how can I solve differentiation?
Sir Reply
with the help of different formulas and Rules. we use formulas according to given condition or according to questions
CALCULUS
For example any questions...
CALCULUS
v=(x,y) وu=(x,y ) ∂u/∂x* ∂x/∂u +∂v/∂x*∂x/∂v=1
log tan (x/4+x/2)
Rohan
what is the procedures in solving number 1?
Vier Reply
Practice Key Terms 7

Get the best Calculus volume 1 course in your pocket!





Source:  OpenStax, Calculus volume 1. OpenStax CNX. Feb 05, 2016 Download for free at http://cnx.org/content/col11964/1.2
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Calculus volume 1' conversation and receive update notifications?

Ask