Latihan BAB 4

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Nama Mahasiswa : Muhammad Mumtaz Syahrie Jahidy

NIM : 220605110072

Kelas : C

Mata Kuliah : Kalkulus

Dosen Pengampuh : Prof.Dr.Suhartono,M.Kom

Jurusan : Teknik Informatika

Universitas : UIN Maulana Malik Ibrahim Malang

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library("mosaicCalc")

## Loading required package: mosaic

## Registered S3 method overwritten by 'mosaic':
##   method                           from   
##   fortify.SpatialPolygonsDataFrame ggplot2

## 
## The 'mosaic' package masks several functions from core packages in order to add 
## additional features.  The original behavior of these functions should not be affected by this.

## 
## Attaching package: 'mosaic'

## The following objects are masked from 'package:dplyr':
## 
##     count, do, tally

## The following object is masked from 'package:Matrix':
## 
##     mean

## The following object is masked from 'package:ggplot2':
## 
##     stat

## The following objects are masked from 'package:stats':
## 
##     binom.test, cor, cor.test, cov, fivenum, IQR, median, prop.test,
##     quantile, sd, t.test, var

## The following objects are masked from 'package:base':
## 
##     max, mean, min, prod, range, sample, sum

## Loading required package: mosaicCore

## 
## Attaching package: 'mosaicCore'

## The following objects are masked from 'package:dplyr':
## 
##     count, tally

## 
## Attaching package: 'mosaicCalc'

## The following object is masked from 'package:stats':
## 
##     D

4.1.4 Latihan

4.1.4.1 Latihan 1

Memecahkan persamaan sin(cos(x2)−x)−x=0.5 for x.{0.0000,0.1328,0.2098,0.3654,0.4217}

JAWAB:

findZeros( sin(cos(x^2) - x) -x - 0.5 ~ x, xlim=range(-10,10))

##        x
## 1 0.2098

4.1.4.2 Latihan 2

Temukan nol dari fungsi ini

yaitu antara t=1 dan t=10.

1. Tidak ada angka nol dalam interval tersebut.}

2. Tidak ada angka nol sama sekali!}

3. $ 2, 4, 6, 8$}

4. $ 1, 3, 5, 7, 9$}

5. {1,2,3,,5,6,7,8,9}

JAWAB :

findZeros( 3*exp(-t/5)*sin(pi*t) ~ t, xlim=range(1,10))

##    t
## 1  0
## 2  1
## 3  2
## 4  3
## 5  4
## 6  5
## 7  6
## 8  7
## 9  8
## 10 9

4.1.4.3 Latihan 3

Gunakan untuk menemukan nol dari masing-masing polinomial ini:findZeros()

1. 3x^2+7x−10

Di mana angka nolnya?

a.x= − 3.33 atau 1

2. x=3.33 atau 1

3. x=−3.33 atau −1

4. x=3.33 atau −1

5. Tidak ada nol

JAWAB:

findZeros( 3*x^2 + 7*x - 10 ~ x, xlim=range(-100,100))

##         x
## 1 -3.3334
## 2  1.0000

2. 2x3−4x2−3x−10

Manakah dari ini yang nol? {-1.0627,0,1.5432,1.8011,2.1223,3.0363,tidak ada}

JAWAB :

findZeros(2*x^3 - 4*x^2 - 3*x - 10 ~ x, xlim=c(-10,10))

##        x
## 1 3.0363

3. 7x4−2x3−4x2−3x−10

Manakah dari ini yang nol? {-1.0627,0,1.5432,1.8011,2.1223,3.0363,tidak ada}

JAWAB :

findZeros( 7*x^4 -2*x^3 - 4*x^2 - 3*x - 10 ~ x, xlim=c(-10,10))

##         x
## 1 -1.0628
## 2  1.4123

4. 6x5−7x4−2x3−4x2−3x−10

Manakah dari ini yang nol? {-1.0627,0,1.5432,1.8012,2.1223,3.0363,tidak ada}

JAWAB :

findZeros( 6*x^5-7*x^4 -2*x^3 - 4*x^2 - 3*x - 10 ~ x, xlim=c(-10,10))

##        x
## 1 1.8012

Daftar Pustaka

https://dtkaplan.github.io/RforCalculus/solving.html