Math 2: Problem Set

The population in a certain city is 50,000 and is increasing at a rate
numerically equal to the square root of the population. What will be the population 20 years hence?
a. 55,987
b. 57,980
c. 54,571
d. 69,420

What is the slope of the graph y = -x^2 at points (2,3)?
a. -4
b. -2
c. 3
d. 1

if a is a simple constant, what is the derivative of y = x^a?
a. x^a-1
b. (a - 1)x
c. ax
d. ax^a-1

D., simple derivation

Find the area of the curve bounded by y = 9 - x^2 and the x-axis.
a. 42
b. 76
c. 36
d. 56

Find the maximum value of y given: y = x^3 - 9x^2 + 15x - 3
a. (1, 4)
b. (3, -12)
c. (2, -1)
d. (5, -28)

What is the point of inflection of the curve x - ln (x)?
a. no point of inflection
b. (1, 0)
c. (1, 5)
d. (1, 1)

If y = arctan (ln x) find the derivative of y at x = 1/e
a. 1.63
b. 1.57
c. 1.45
d. 1.36

Newton's method is being used to find the roots of the equation f(x) = (x-2)^2 -1. What is the third approximation of the root if 9.33 is chosen as the first approximation?
a. 2.0
b. 1.0
c. 4.0
d. 3.0

The rate of population growth of a country is proportional to the number of inhabitants. If a population of a country now is 40 million and is expected to double in 25 years, how many years will the population be 3 times the present?
a. 39.62 years
b. 43.34 years
c. 42.69 years
d. 25.45 years

A certain radioactive substance has a half-life of 38 hrs. Find how long it takes for 90% of the radioactivity to be dissipated.
a. 126.5 hrs
b. 145.7 hrs
c. 135.7 hrs
d. 130.7 hrs

Solve the constant of integration of the given differential equation xdx +6y^5dy = 0. Considering x = 0 and y = 2
a. 46
b. 54
c. 64
d. 120

_ is also known as the composite function rule.
a. Chain rule
b. Constant rule
c. Power rule
d. Product Rule

The cost, C, of a product is a function of the quantity x of the product. Find the quantity for which the cost is minimum. C(x)=x²-4000x+50
a. 2000
b. 4200
c. 6900
d. 1000

just use calcu