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Engineering Computations One: Differential and Integral Calculus Questions: 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 temperature. 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 P? 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

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Differential and Integral Calculus
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