Calculus 201, calculus homework help

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nlcuky

Mathematics

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2 Page calculus worksheet I need each problem worked out thoroughly so I can study each problem.

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5) Solve the following questions below. (15 points) a) An investment of $4000 is made at an annual interest rate of 5%. Interest is compounded every month. How much money will there be at the end of 5 years? b) A person wants to put enough money in the bank to have $6000 at the end of 8 years. The bank pays 4% annual interest compounded quarterly. How much money does the person need to put in the bank to reach his goal? c) A bank pays 2% interest compounded monthly. What is its effective interest rate? d) If you invest $1,000 at an annual interest rate of 5% compounded continuously, calculate the final amount you will have in the account after five years. e) If you invest $500 at an annual interest rate of 10% compounded continuously, calculate the final amount you will have in the account after five years. 6) Use laws of logarithms to Expand and simplify expression. (15 Points] a) f(x) = log x(x + 1) b) f(x) = In xye*2 √x-2 c) f(x) = log x3 + 2 х?у e) f(x) = Inx(x + 1)(x + 2) d)f(x) = log 7) Write each expression as a logarithm of a single quantity (15 points] a) 4 Ina - 5 In b b) In x - 2 lnb + 7 Inc c) Ina + In b - 2 Inc d) 5 Ina + 6 In b + 7 Inc e) 3 Ina - (2 lnb + 2 Inc) MATH 201 5/8/2017 1) Sketch the graph off&g: f(x) = 3% g(x) = log3x (10 points] 10- 15 10 15 2) Differentiate the following functions. (15 points) a) f(x) = xe2x b) f(x) = xe-x^ c) f(x) = (1 + e-2x) d) f(x) = V6e-x + 2x ex² e) f(x) = x 3) Differentiate the following functions. [ 15 points) a) f(x) = ln x b) f(x) = In (x3 + 1) c)f(x) = 3x2 In 2x d) f(x) = In V e) f(x) = 4) Differentiate the following functions. (15 points) a) f(x) = In(e4x + 3) b) f(x) = In(ex? +1) In x c) f(x) = 1 + ex ex² e) f(x) = lne d) f(x) = 1 + In x
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Explanation & Answer

Hi again, please see my solutions attached in a PDF! Let me know if you need anything else or have any other questions. 😎 And, of course, let me know if you ever need help with calculus or other subjects again. Best of luck! 💪

Calculus 201 for ayphxl
Studypool Tutor jmmanley

Problem 1
Sketch the graph of f & g: f (x) = 3x , g(x) = log3 x. See the plot of the graphs below:

Figure 1: In black: f (x) = 3x . In blue: f (x) = log3 (x) = log(x)/ log(3).

Problem 2
Differentiate the following functions.

a.
f (x) = xe2x
f 0 (x) = x(2e2x ) + e2x = (2x + 1)e2x

b.
f (x) = xe−x
2

2

2

f 0 (x) = x(−2xe−x ) + e−x = (1 − 2x2 )e−x

2

c.
f (x) = (1 + x−2x )4
d
d
d
(1 + x−2x ) = 4(1 + x−2x )3 (x−2x ) = 4(1 + x−2x )3 e−2x log(x)
dx
dx
dx
d
d
f 0 (x) = −8(1 + x−2x )3 e−2x log(x) (x log(x)) = −8(1 + x−2x )3 x−2x (x log x + log x)
dx
dx

f 0 (x) = 4(1 + x−2x )3

f 0 (x) = −8x−2x (1 + x−2x )3 (1 + log x)

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Page 1 / 5

d.
f (x) =

p
6e−x + 2x

1
1 − 3e−x
f 0 (x) = (6e−x + 2x)−1/2 (−6e−x + 2) = √
2
6e−x + 2x

e.
2

f (x) =

ex
x

2

2xex2 ex
2
f (x) =
− 2 = (2 − x−2 )ex
x
x
0

Problem 3
Differentiate the following functions.

a.
f (x) = ln x8
f 0 (x) =

1 7
8
8x =
8
x
x

b.
f (x) = ln(x3 + 1)
f 0 (x) =

1
3x2
2
3x
=
x3 + 1
x3 + 1

c.
f (x) = 3x2 ln x
f 0 (x) = 6x ln x + 3x2

1
= 3x(1 + 2 ln x)
x

d.
f (x) = ln



x

1
1
1 1
f 0 (x) = √ (x)−1/2 = √ √ =
2x
x2
2 x x

e.
This is the same as subsection e in problem 1. Please see above.

Problem 4
Differentiate the following functions.

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Page 2 / 5

a.
f (x) = ln(e4x + 3)
1
4e4x
4x
4e
=
e4x + 3
e4x + 3

f 0 (x) =

b.
2

f (x) = ln(ex + 1)
2

f 0 (x) =

1
2xex
x2
2xe
=
ex2 + 1
e x2 + 1

c.
f (x) =
f 0 (x) =

ln x
1
= ln x
x
1+e
1 + ex

1 1
1
1
ex ln x
x
−...


Anonymous
Just what I needed…Fantastic!

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