Concept explainers
Matching In Exercises 57–-60, match the
are labeled (a), (b), (c), and (d).]
a).
b).
c).
d).
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Calculus
- Comparing Ay and dy In Exercises 7-10, use the informa- tion to evaluate and compare Ay and dy. Function x-Value Differential of x 7. y = x³ x = 1 Ax = dx = 0.1arrow_forwardColue the differential equation de |ती- FParrow_forwardExperimental data on the nitrogen content of soil samples taken from a field used for vegetation was modeled to show a simple algebraic curve. This curve is represented by dy d²y the functions below. Find and of the curve. dx dx2 x = u3 – 4u? 5, у%3D Зи? 2и -arrow_forward
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- Exercises. 1. (a) Find the differential of g(u, v) = u? + uv. (b) Use your answer to part (a) to estimate the change in g as you move from (1,2) to (1.2, 2.1).arrow_forwardFree fall An object in free fall may be modeled by assuming the only forces at work are the gravitational force and air resistance. By Newton's Second Law of Motion (mass · acceleration = the sum of external forces), the velocity of the object satisfies the differential equation m. v'(t) = mg + f(v), mass acceleration external forces where f is a function that models the air resistance (assuming the positive direction is downward). One common assumption (often used for motion in air) is that f(v) = -kv², for t > 0, where k > 0 is a drag coefficient. a. Show that the equation can be written in the form k v'(1) = g – av², where a = =. b. For what (positive) value of v is v'(t) = 0? (This equilibrium solution is called the terminal velocity.) marrow_forwardDetermine whether the functions y, and y, are linearly dependent on the interval (0,1) y=1-2 sint, y, = 12 cos 2t Select the correct choice below and, if necessary, fill in the answer box within your choice. O A. Since y, = ( )y½ on (0,1), the functions are linearly dependent on (0, 1). (Simplify your answer.) O B. Since y,= ( )y½ on (0,1), the functions are linearly independent on (0,1). (Simplify your answer ). OC. Since y, is not a constant multiple of y, on (0,1), the functions are linearly independent on (0, 1) O D. Since y, is not a constant multiple of y, on (0,1), the functions are linearly dependent on (0,1).arrow_forward
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