Calculus Answers

Find the relative extrema using both First and Second Partial Derivative test
fx=1+8x-3x2

A function f:[a,b]–R is defined as
f(x) = 4 if x is rational
f(x) = -3 if x is irrational
Check whether f is integrable on [a,b]. Justify your answer

The equation is:
v(t)=A(1- e^(-t/t_maxspeed ) )
The tasks are to:
● Use thinking methods to analyse the given engineering problem, e.g. break the problem down into a series of manageable elements, and produce a specification

An electric circuit consisting of an electromotive force V, a resistance R and an inductor L. The current I at time t is given by:
I=(V/R(1-e^-Rt/L))

When the voltage is first applied (at t=0) the inductor opposes the rate of increase of current and I is small, however as t increases, I approaches V/R
(a) If L is the only independent variable, determine lim(I)
L 0
(b) If R is the only independent variable, determine lim(I)
R 0

apply implicit differentation to determine dy/dx
a) In(sin^-1(e^x)+yx^2=1
b) tan^-1(x+y)-sin^-1(e^y+x)=4

Use appropriate software to sketch each of the following surfaces and identify it.
4(x+1)^2 +2(y-2)^2 +(z-1)^2=1

4(x+1)^2 +2(y-2)^2 +(z-1)^2=1