Latihan BAB 4

Muhammad Yasril Adim Al Amin

NIM : 220605110070

KELAS : C

MATKUL : KALKULUS

DOSEN PENGAMPU : Prof.Dr.Suhartono,M.Kom

JURUSAN : TEKNIK INFORMATIKA

LEMBAGA : UNIVERSITAS ISLAM NEGERI MAULANA MALIK IBRAHIM MALANG

==== LATIHAN 1 ====

Selesaikan persamaan sin(cos(x^2)-x)-x = 0.5 untuk x.{0.0000,0.1328,0.2098,0.3654,0.4217}

= JAWAB =

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

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

##        x
## 1 0.2098

==== LATIHAN 2 ====

Temukan nol dari fungsi tersebut 3e^-t/5 sin(2π/2.t), yang berada diantara t = 1 dan t = 10 a. Tidak ada nol dalam interval itu b. Tidak ada nol sama sekali c. $ 2, 4, 6, 8 $ d. $ 1, 3, 5, 7, 9 $ e. {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 3 ====

Gunakan findzeros() untuk mencari untuk menemukan nol dari masing-masing polinomial ini: 1. 3x^2 + 7x - 10

Dimana angka nolnya? a. sebuah x = -3.33 atau 1 b. x = 3.33 atau 1 c. x = -3.33 atau -1 d. x = 3.33 atua -1 e . tidak ada nol

= JAWAB =

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

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

2. 4x^2-2x+10

Dimana angka nolnya? a. sebuah x = -3.33 atau 1 b. x = 3.33 atau 1 c. x = -3.33 atau -1 d. x = 3.33 atua -1 e . tidak ada nol

= JAWAB =

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

##        x
## 1 3.0363

3. 7x^4-2x3-4x^2-3x-10

Dimana angka nolnya? {-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. 6x^5-7x4-2x^3-4x2-3x-10

Dimana angka nolnya? {-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

Sumber Referensi : https://dtkaplan.github.io/RforCalculus/graphing-functions.html