(1 pt) Suppose that f(x) = x(ln(x))19. Find f'(2)| f'(2) = (1 pt) A 18| ft...
(1 point) A conical tank has height 3 m and radius 2 m at the top. Water flows in at a rate of 0.9m°/min. How fast is the water level (h) rising when h = 2.7 m? The speed of the water level rising is = 0.09 m/min (1 point) A hot air balloon rising vertically is tracked by an observer located 5 km from the lift-off point. At a certain moment, the angle between the observer's line-of-sight and the...
1. Recall that the elasticity of demand is defined by E(p) = −pf0 (p) f(p) ( a) Let the demand equation for hand sanitizer be given by f(p) = p 20 − p 2 Find E(p) and then compute E(4). (b) If E(p) = 1.5, interpret what this would mean for the selling of hand sanitizers. 2. Suppose the demand of mathematical textbooks is given by the equation d(x) = x 2 + 6x + 2 (a) State the revenue...
Math 2413 Derivative Applications Assignment Due: Tuesday, June 18, 2019 (5:30 pm) Name Show all work. Label your answers with the proper units. (3 points each ) A spherical ball is being inflated at the rate of 12 cubic inches per second. Find the rate at which the radius of the sphere is growing when the radius is 2 inches. long. 2. A 13 foot ladder is leaning against a wall. The base of the ladder is being palled away...
Math 131 Extra Credit Assignment Page 2 of 2 March 2019 2. Suppose f(x) 1. (a) (1 point) Using the definition of the derivative, find f'(). (b) (1 point) Find the equation of the line tangent to f(x) at the point on the graph where 3. Find the derivative of the following functions (a) (1 point) +x f(x) (a-7)10 (b) (1 point) Find y' if y5+1Y=1+14y. 4. (1 point) A man uses a ladder that is 29 feet in length...
(18 pts) Find the absolute extreme values of f(x) = 2 cos x - sin 2x on [0, 21). (24 pts) If a ball is thrown vertically upward with a velocity of 160 feet per second, then its height after t seconds is h(t) = -16t2 + 160t. a. Find the average velocity of the ball during the first 5 seconds. b. Use the Mean Value Theorem to verify that at some time during the first 5 seconds the instantaneous...
C, D, F??????? A partidle moves according to a law of motion s-t), t0, where t is measured in seconds and s in feet. (If an answer does not exist, enter DNE.) ft) - - 721t (a) Find the velocity at time t -32-14 +21 ft/s (b) What is the velocity after 1 second? 1)10 ft/s (c) When is the particle at rest? t 2.33333333 | X (d) when is the particle moving in the positive direction? (Enter your answer...
This Question: 1 pt 2 of 3 Let f(x) = x + 2 and g(x)=x²-x. Find and simplify the expression. (f+g)(2) (f+9)(2) = (Simplify your answer.)
At time t = 1, a particle is located at position (x, y) = (3, 2). If it moves in the velocity field F(x, y) = xy − 1, y2 − 9 find its approximate location at time t = 1.04.
Exercises 1. Suppose a force acts on a 4.00 kg object in the x-direction. The force varies with time and is given by F(t)12.0t3 - 8.00 N. At t -0, the object has a velocity of 3.00 m/s in the positive x-direction. Use the impulse-momentum theorem to find the object's velocity after 2.00 s. 2. In a lab experiment, a spring gun projects a metal sphere. The sphere leaves the spring gun with a velocity of 3.00 m/s in the...
1. (2 marks) If y = 3x and x changes from 1.2 to 2.5: a) What is the average change in y? b) What is the instantaneous rate of change in y when x = 2.0? 2. (2 marks) The value "V" (in dollars) of a new laptop t years after it is purchased is given by the function: V(t) = 899.95e -0.71 a) What is the average rate of change of the value during the first two years? Round...