Find the increment and differential of each of the following functions for the given values of thevariables and their increments.15. x In y + y In x; x = y = 1, Ax = 0.01, Ay = 0.0216. y tan-1 xy; x = 2, y = 0.5, Ax = –0.05, Ay = 0.0117. Find, approximately, the amount of metal in a closed tin can 3 inches in diameter and 5 incheshigh, if the metal is 1/32 inches thick.18. Find by use of differentials the approximate total area of a right circular cone whose base radiusand height are 5.03 inches and 11.89 inches, respectively.

we have use total differential For a function z= f(x,y) dz=∂z∂xdx +∂z∂ydy Note : One question is…

Answered: Find the increment and differential of…

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter6: Exponential And Logarithmic Functions

Section6.1: Exponential Functions

Problem 60SE: The formula for the amount A in an investmentaccount with a nominal interest rate r at any timet is...

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The formula for the amount A in an investmentaccount with a nominal interest rate r at any timet is given by A(t)=a(e)rt, where a is the amount ofprincipal initially deposited into an account thatcompounds continuously. Prove that the percentageof interest earned to principal at any time t can becalculated with the formula I(t)=ert1.
Near the surface of the moon, the distance that an object falls is a function of time. It is given by d(t)=2.6667t2 , where t is in seconds and d(t) is in feet. If an object is dropped from a certain height, find the average velocity of die object from t=1tot=2 .
= 8. A room is initially at the outdoor temperature of 25°C. Now a large fan that consumes 200 W of electricity when running is turned on. The heat transfer rate between the room and the outdoor air is given as QUA(TI- To) where U = 6 W/m2 °C is the overall heat transfer coefficient, A= 30 m² is the exposed surface area of the room, and T₁ and To are the indoor and outdoor air temperatures, respectively. Determine the indoor air temperature when steady operating conditions are established. Fan
Find the second derivative
a) Determine the rate of change for the following functions (i) to (iii): B=10 B is the value 10i. y = Bx3 – Bx^-2 + 9 Determine the rate of change o y with respect to xii. s = ln(Bsin2t)Determine the rate of change of s with respect to tiii. y = Bx^2 cosxDetermine the rate of change of y with respect to x
There are compartments in the vehicle that fill up with water, so that the vehicle is heavy enough to travel underwater. The relation between the weight of the compartment as it fills with water and the time elapsed is given in the table below. Check the boxes that correspond to the correct statements. y: Weight of compartment (in Ib) The rate at which the compartment fills with water is constant. x: Time (in min) Every successive minute, the compartment becomes twice its weight in the previous minute. 9. The empty weight of the compartment is 3 lb. 24 The compartment weighs 2 Ib at 0 min. 0000 12 1, 2. 3.
Suppose that y = C(t) represents the average cost of a gallon of milk in the United States t years since 1980. What does AC represent? Δι
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