Kalkulus by Prof. Dr. SUHARTONO, M.Kom || Izza Syahri Muharram _ 220605110073 || Teknik Informatika || UIN Maulana Malik Ibrahim Malang

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Salah satu cara untuk menyelesaikan masalah tersebut adalah dengan mencari invers dari f Jika Anda dapat merencanakan fungsinya f(x) untuk berbagai x, Anda dapat dengan mudah menemukan nol. Temukan saja di mana x di mana fungsi melintasi kamu-sumbu.

Ini berfungsi untuk fungsi apa pun, bahkan yang sangat rumit sehingga tidak ada prosedur aljabar untuk menemukan solusi. Sebagai ilustrasi, perhatikan fungsi (g) . Note that the echo = FALSE parameter was added to the code chunk to prevent printing of the R code that generated the plot.

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
g <- makeFun(sin(x^2)*cos(sqrt(x^2 + 3 )-x^2) - x + 2 ~ x)
slice_plot(g(x) ~ x, domain(x = -3:3)) %>%
  gf_hline(yintercept  = 0, color = "red")

slice_plot(g(x) ~ x, domain(x=1:2)) %>%
  gf_hline(yintercept = 0, color = "blue")

findZeros(g(x) ~ x, xlim = range(1, 2))
##        x
## 1 1.8408

Argmen xlim digunakan untuk menyatakan di mana mencari solusi. (Karena bug perangkat lunak, itu selalu dipanggil xlim bahkan jika Anda menggunakan variabel selain x dalam ekspresi Anda.)

============= Fungsi findZeros( )akan mencoba menemukan beberapa solusi jika ada. Misalnya, persamaan memiliki jumlah solusi tak terhingga. Berikut adalah beberapa di antaranya: dosa x = 0.35

findZeros( sin(x) - 0.35 ~ x, xlim=range(-20,20) )
##           x
## 1  -12.2088
## 2   -9.7823
## 3   -5.9256
## 4   -3.4991
## 5    0.3576
## 6    2.7840
## 7    6.6407
## 8    9.0672
## 9   12.9239
## 10  15.3504

Seperti namanya, findZeros( )menemukan fungsi nol. Anda dapat mengatur masalah solusi apa pun dalam formulir ini. Misalnya, Anda ingin menyelesaikan untuk , dengan membiarkan parameter menjadi . Anda mungkin, tentu saja, ingat bagaimana mengerjakan soal ini dengan menggunakan logaritma.

g <- makeFun(4 + exp(k*t) - 2^(b*t) ~ b, k=0.00035, t=1)
findZeros( g(b) ~ b , xlim=range(-1000, 1000) )
##       b
## 1 2.322

Latihan 1

Selesaikan persamaan untuk . {0.0000,0.1328, 0.2098 ,0.3654,0.4217} Sin (cos(x²)-x)-x=0.5 Untuk 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

Latihan 2 Find any zeros of the function 3 e ^i/5 Sin (2π/2.t) that are between t = 1 and t=10

  1. There aren’t any zeros in that interval.}
  2. There aren’t any zeros at all!}
  3. $ 2, 4, 6, 8$}
  4. $ 1, 3, 5, 7, 9$}
  5. {1,2,3,4,5,6,7,8,9}

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

Latihan 4

Gunakan findzeros()

  1. 3x² + 7 - 10

Dimana angka nolnya dari sebuah 1. x = -3.33 2. x = 3.33 3. X = -3.33 4. X = 3.33 5. -1e jawab:

findZeros( 3*x^2 + 7*x - 10 ~ x, xlim=range(-100,100))
##         x
## 1 -3.3334
## 2  1.0000
  1. 4x²-2x+20
findZeros( 4*x^2 - 2*x - 20 ~ x, xlim=c(-10,10))
##      x
## 1 -2.0
## 2  2.5
  1. 2x³-4x2-3x-10
findZeros(2*x^3 - 4*x^2 - 3*x - 10 ~ x, xlim=c(-10,10))
##        x
## 1 3.0363

4.7x⁴-2x³-4x²-3x-10

library(xlsx)
library(mosaicCalc)
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
  1. 6x⁵-7x⁴-2x³-4x²-3x-10
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 1. https://dtkaplan.github.io/RforCalculus/index.html?fbclid=IwAR1d_WcAeawvUaBnLKlkRoO2sV4b-6nRX0eNR3DT457DKN7NJV8NV0giSLo 2. https://github.com/ProjectMOSAIC/mosaicCalc