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Lab #2 - Solutions


Topics in this lab

Introduction

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>> format long

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Exercise 1

>> f = @(x) tanh(x/10)
f = 

    @(x)tanh(x/10)

>> f(2*pi)
ans =

   0.556893306900211

>> f(-exp(1))
ans =

  -0.265325141803780

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Exercise 2

>> h = @(x) (3*x^3 - 1)/(x^2 + 3)
h = 

    @(x)(3*x^3-1)/(x^2+3)

>> h(sqrt(3)*i)
ans =

     -2.251799813685248e+15 - 3.510208517199282e+16i

>> h(nthroot(1/3,3))
ans =

    -6.379217526741067e-17

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Exercise 3

>> s = @(t) cos(t)
s = 

    @(t)cos(t)

>> q  = @(t) 1/(s(t)^2 + 1)
q = 

    @(t)1/(s(t)^2+1)

>> q(pi)
ans =

   0.500000000000000

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Exercise 4

>> T = @(x,y) 5/x^2 - 1 + y + 0.5*x^2/y
T = 

    @(x,y)5/x^2-1+y+0.5*x^2/y

>> T(exp(pi),nthroot(5,4))
ans =

     1.795571125088599e+02

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Exercise 5

>> f = @(x) cos(x)
f = 

    @(x)cos(x)

>> g = @(x) x^2
g = 

    @(x)x^2

>> h = @(x) f(x)*g(x)
h = 

    @(x)f(x)*g(x)

>> fp = @(x) -sin(x)
fp = 

    @(x)-sin(x)

>> gp = @(x) 2*x
gp = 

    @(x)2*x

>> hp = @(x) f(x)*gp(x) + fp(x)*g(x)
hp = 

    @(x)f(x)*gp(x)+fp(x)*g(x)

>> hp(-4.561)
ans =

 -19.189089745181988

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Exercise 6

>> distance = @(x1,y1,x2,y2) sqrt((x1-x2)^2 + (y1-y2)^2)
distance = 

    @(x1,y1,x2,y2)sqrt((x1-x2)^2+(y1-y2)^2)

>> distance(0,cos(0),pi,cos(pi))
ans =

   3.724191778237173

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Exercise 7

  • Earth : 1.0832e+12 or 1.08 trillion cubic meters
  • Mars : 1.63190e+11 or 163 billion cubic meters
  • Jupiter : 1.4313e+15 or 1.43 quadrillion cubic meters

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Exercise 8

Density of dry air at sea level for different temperatures

  • 0 C : 1.2922
  • 10 C : 1.2466
  • 20 C : 1.2041
  • 30 C : 1.1644

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Get the code

Do you want to try the above code fragments on your own? Download the Matlab script that produces this page here. (lab_2_solns.m)

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