Calculus Answers

Find the extreme values of

x^4+y^4-2(x-y)^2

The adiabatic law (no gain or heat loss) for the expansion of air is PV 1.4 = C, where P is the pressure in lb/in^2, V is the volume in cubic inches, and C is a constant. At a specific instant, the pressure is 40 lb/in^2 and is increasing at the rate of 40 lb/in^2 each second. If C = 5/16, what is the rate of change of the volume at this instant?

U= (x^2+y^2+z^2)^m/2 find value of m Uxx+Uyy+Uzz=0

1. Evaluate the limit by first recognizing the sum as a Reimann Sum for a function defined on [0,1] limit as n tends to infinity 1/n (the root of 1/n + root of 2/n + root of 3/n +....+ root of n/n)

2. If f prime is continuous on [a,b], show that 2* the integral from a to b of f(x) f prime(x) dx= f(b) square minus f(a) square.

Use apsolen delta definition to show that lim x approches to -2 for f(x) 1÷x+1=-1

find the approximate value of ∛127

MR=6+10x-18x^2

X=1

Sh 4000

Find total revenue

find the limit lim x→0 x^2 cos 1/x.

find the limit lim x→0 x^2 cos 1/x.

{F} The equation for a displacement 𝑠(𝑚), at a time 𝑡(𝑠) by an object starting at a displacement of 𝑠0 (𝑚), with an initial velocity 𝑢(𝑚𝑠 −1 ) and uniform acceleration 𝑎(𝑚𝑠 −2 ) is: 𝑠 = 𝑠0 + 𝑢𝑡 + 1 2 𝑎𝑡 2 A projectile is launched from a cliff with 𝑠0 = 30 𝑚, 𝑢 = 55 𝑚𝑠 −1 and 𝑎 = −10 𝑚𝑠 −2 . The tasks are to: a) Plot a graph of distance (𝑠) vs time (𝑡) for the first 10s of motion. b) Determine the gradient of the graph at 𝑡 = 2𝑠 and 𝑡 = 6𝑠. c) Differentiate the equation to find the functions for: i) Velocity (𝑣 = 𝑑𝑠 𝑑𝑡) ii) Acceleration (𝑎 = 𝑑𝑣 𝑑𝑡 = 𝑑 2 𝑠 𝑑𝑡2 ) d) Use your results from part c to calculate the velocity at 𝑡 = 2𝑠 and 𝑡 = 6𝑠. e) Compare your results for part b) and part d). f) Find the turning point of the equation for the displacement 𝑠 and using the second derivative verify whether it is a maximum, minimum or point of inflection. g) Compare your results from f) with the graph you produced in a).