Engineering Computations One:
Differential and Integral Calculus
1. Biologists have noticed that the chirping rate of crickets of a certain species
is related to temperature, and the relationship appears to be very nearly
linear. A cricket produces 113 chirps per minute at 21°C and 173 chirps
per minute at 27°C.
(a) Find a linear equation that models the temperature T as a function
of the number of chirps per minute N.
(b) What is the slope of the graph and what does it represent?
(c) What is the T-intercept of the graph and what does it represent?
(d) If the crickets are chirping at 150 chirps per minute, estimate the
2. Consider the piecewise function f(x) = tand if
(a) Sketch a graph of f.
(b) State the domain and range of f.
(c) Does f have an inverse? If not, explain why, otherwise if so then
sketch the inverse function 8-1.
3. Find the domain of the function g(t) =
4. Is the function given by f(x) = (r - 5)(x + 5)r evem or odd or neither?
Please justify your reasoning.
5. Factorize the quintic polynomial P(x) = 2-5472-22 18: into a
product of irreducible linear and quadratic factors. What are the roots of
6. Comsider the rational function g(t) =
(a) What is the domain of g?
(b) Given that g is one-to-one, find the inverse g-¹.
(c) What is the range of g?
7. Use partial fractions to simplify the rational function
8. Solve the equation 2sin2r-sinz= 1
This material may consist of step-by-step explanations on how to solve a problem or examples of proper writing, including the use of citations, references, bibliographies, and formatting. This material is made available for the sole purpose of studying and learning - misuse is strictly forbidden.