Calculus Answers

Evaluate the function at the indicated value, using the technique indicated. Show work.
: Divide. Use synthetic division, if possible.

(x^4 + 6x^3 – x^2 – 5x + 1) ÷ (x-2)

Evaluate the function at the indicated value, using the technique indicated. Show work.
: Divide. Use synthetic division, if possible.

(x^3 + 9x^2 – 5x + 11) ÷ (x^2 + 2)

Evaluate the function at the indicated value, using the technique indicated. Show work.
: Find m(5) using direct substitution: m(x)=x^2 + x – 1

Evaluate the function at the indicated value, using the technique indicated.
: Find w(-3) using synthetic substitution: w(x) = 11x^3 – 6x^2 + 2

1: If you deposit $1,000 into an account that pays 4% interest compounded continuously, how long will it take the account to grow to $2,000? Show work. answer 17.3 years.

2: If you pour a cup of coffee that is 200degrees F, and set it on a desk in a room that is 68Degrees F, and 10 minutes later it is 145degrees F, what temperature will it be 15 minutes after you originally poured it? Show work. answer 126.8 Degrees F

3: The radioactive substance krypton-91 has a very short half-life of about 10 seconds. What is the decay constant for this substance? Show work. answer 0.0693.

: The x-intercept of the graph of f(x) = 3log(x-5) + 2 is:

A: 10^2/3 -5
B: 10^-2/3 -5
C: 10^-2/3 +5
D: 10^2/3 +5


: The population (in millions) of a certain country can be approximated by the function:
p(x) = 100 ∙ 1.02^x

Where x is the number of years after 2000. Which of the following calculations will tell in what year the population can be expected to reach 300 million?

A: In(3)/In(1.02)
B: In(3/1.02)
C: In(3)/In(1.02) + 2000
D: In(3/1.02) + 2000

: Solve for x:
150 = 50e^7x

A: x = 1/e
B: x = In(3) – 7
C: x = In(3)/7
D: x = In(150)/7 ∙ In(50)

: Solve for x:
3500 = 700 ∙ 2^8x
Check all that apply.

X = log(5)/8

x = In(5)/8 ∙ In(2)

x = log(5)/ 8 ∙ log(2)

x = In(8)/5

: The vertical asymptote of the function y = In(x-6) + 5 is:

A: x = -5
B: x = 5
C: x = -6
D: x = 6

: For the function y = In(x + 1) + 5, Which of the following statements are true?

A: The domain is (-1,∞), and the range is all real numbers
B: The domain is all real numbers, and the range is [5,∞).
C: The domain is (1,∞), and the range is [5,∞ ).
D: The domain is (1,∞), and the range is all real numbers.

Logarithmic function

1: e^in(6x) =

A: In(x)
B: 6x
C: 6In(x)
D: In(6)


2: log(10^6 x^2) =

A: 12
B: 6x^2
C: 6+2log(x)
D: 12log(x)

Give the chemistry equation and the calculus derivative formula for solving the ozone depletion.

Please help me this question
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