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

Lembaga : Universitas Islam Negeri Maulana Malik Ibrahim Malang

Fakultas : Sains dan Teknologi

Jurusan : Teknik Informatika

Kelas : (C) Kalkulus

NIM : 230605110078

# import the data
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
## The legacy packages maptools, rgdal, and rgeos, underpinning the sp package,
## which was just loaded, will retire in October 2023.
## Please refer to R-spatial evolution reports for details, especially
## https://r-spatial.org/r/2023/05/15/evolution4.html.
## It may be desirable to make the sf package available;
## package maintainers should consider adding sf to Suggests:.
## The sp package is now running under evolution status 2
##      (status 2 uses the sf package in place of rgdal)
## 
## Attaching package: 'mosaicCalc'
## The following object is masked from 'package:stats':
## 
##     D

Zero finding

Fungsi adalah mekanisme untuk mengubah masukan tertentu menjadi keluaran. Penemuan nol berarti melakukan sebaliknya: jika diberi nilai keluaran, cari masukan yang sesuai. Sebagai contoh, perhatikan fungsi eksponensial \(e^x\). Diberikan masukan tertentu, katakanlah \(x = 2.135\) Anda dapat dengan mudah menghitung output yang sesuai:

exp(2.135)
## [1] 8.457047
## [1] 8.457047
log(4.93)
## [1] 1.595339
## [1] 1.595339

Grafis penemuan nol

Misalkan Anda mungkin memiliki suatu fungsi \(h(x)\) yang Anda buat dengan kombinasi linier dan/atau perkalian fungsi dan/atau komposisi fungsi.

Langkah-langkah prosesnya adalah:

i. Buat grafik fungsinya \(h(x)\) selama interval domain yang diminati

ii. Gambarlah garis horizontal yang terletak pada nilai di sisi kanan persamaan \(h(x_0) = 3\)

iii. Temukan tempat, jika ada, di mana garis horizontal memotong grafik fungsi tersebut.

Perhatikan gambar berikut :

Temuan angka nol

Kita akan menggunakan fungsi R/mosaik Zeros(). Argumen pertama adalah ekspresi gelombang laut dan argumen kedua adalah interval domain yang akan dicari.

#define the function
f <- rfun(x ~ x, seed=579)
#table of zeros
Zeros(f(x) - 6 ~ x, bounds(x=-4:4))
## # A tibble: 2 × 2
##        x      .output.
##    <dbl>         <dbl>
## 1 -3.82  -0.0000777   
## 2  0.497 -0.0000000835
#grafik
slice_plot(f(x) ~ x, bounds(x=-4:4)) %>%
  gf_hline(yintercept = ~ 10, color="blue")