Calculus Answers

The radioactive isotope gallium-67, used in the diagnosis of malignant tumors, has a biological

𝑡

half-life of 46.5 hours. The half-life of the isotope is modeled as 𝐴 = 𝐴₀ (¹₂)^ℎ , where h is the half-life and t is the time in hours. If we start with 100 milligrams of the isotope, how many milligrams will be left after: 24 hours, and after 1 week? 

A company that operates for 18 hours a day has introduced a new daily wage system that

incorporates variable hourly rate to encourage longer shifts. The company pays $10 for first

hour or any part of the first hour. Afterwards, company pays additional 2% per hour for each

hour or part of each additional hour. Write a piece-wise function that shows the salary as a

function of hours. Also sketch a graph of this function.

Let D = {(x, y) ∈ R

2

: x > 0, 0 < y < x3}. Define

f(x, y) = (

0, (x, y) ∈/ D

1, (x, y) ∈ D.

a) Approaching (0, 0) along the line y = mx for each real number m and the y-axis, prove that

lim(x,y)→(0,0) f(x, y) exists and compute the limit.

b) Argue whether f is continuous at (0, 0).

When two given functions, f(x) = x

2 + 3 and g(x) = 2x − 5, are divided with each other, a

new third function is obtained. Find (f/g)(x) and identify its domain.

Factoring Polynomials Practice:

Use synthetic division to divide polynomials by possible roots

5x³ + 29x + 19x - 5

P= Q=

Factoring Polynomials Practice:

Use synthetic division to divide the polynomials by possible roots

2) 4x³ - 9x² + 6x - 1

P= Q=

Factoring Polynomials Practice:

Use synthetic division to divide polynomials by possible roots

x³ + 4x² + 5x + 2

P= Q=

Unit 1 Review:

8) Which graph of inverse of f(x)?