ESA147 – KALKULUS 1 (DASAR) – Just another Departemen Dukungan Pembelajaran Sites site

MATERI PRESENTASI

RENCANA PEMBELAJARAN SEMESTER

RPS ESA 147 – Kalkulus 1

BAHAN PRESENTASI :

BAHAN PENGAYAAN :

Blog Dosen 1
Blog Dosen 2
Blog Dosen 3

DAFTAR PUSTAKA :

Buku 1
Buku 2
Buku 3

PENILAIAN :

Kehadiran : 10%
Tugas : 20%
UTS : 30%
UAS : 40%

DOSEN PENGAMPU :

5382 – Holder Simorangkir
7400 – Tri Sutrisno
7344 – Gilang Pratama Hafidz

MATERI 7

KEGUNAAN TURUNAN – PERTEMUAN 7

I. Garis Singgung

1. Tentukan gradient garis singgung grafik y = x² – 5x + 6 dititik yang absisnya = 2 dan persamaan garis singgung tersebut.

2. Tentukan persamaan garis singgung grafik x² + y² = 25, dititik yang absisnya = 3 dan ordinatnya positip.

3. Tentukan persamaan garis singgung grafik x² – 2xy + y² – x + 3y + 2 = 0, dititik (0,-2)

II. Fungsi Ekstrim.

4. Petruk dan Bagong membagi uang Rp. 10.000 ,-. Bila bagian Petruk dan bagong dikalikan hasilnya mencapai ekstrim. Berapakah bagian masing-masing ? berapa nilai ekstrimnya ? ekstrim maksimum atau ekstrim minimum ?

5. Kawat sepanjang 1000 meter dipotong menjadi dua bagian, satu bagian dibentuk lingkaran dan satu bagian lagi dibentuk bujur sangkar. Tentukan panjang kawat masing-masing agar jumlah luas bangun yang terbentuk maksimum .

6. Sebuah balok volumenya 72 m³, panjang = 2 kali lebar. Tentukan ukuran balok agar bahan yang digunakan sehemat-hematnya.

7. Sebuah kaleng susu berbentuk silinder, luas silinder = 924 cm². Tentukan ukuran silinder agar volume silinder maksimum.

MATERI 1

MATERI_I

Preliminaries

REAL NUMBERS
A real number may be either rational or irrational; either algebraic or transcendental; and either positive, negative, or zero. Real numbers are used to measure continuous quantities. They may in theory be expressed by decimal representations that have an infinite sequence of digits to the right of the decimal point; these are often represented in the same form as 324.823122147… The ellipsis (three dots) indicate that there would still be more digits to come.

More formally, real numbers have the two basic properties of being an ordered field, and having the least upper bound property. The first says that real numbers comprise a field, with addition and multiplication as well as division by nonzero numbers, which can be totally ordered on a number line in a way compatible with addition and multiplication. The second says that if a nonempty set of real numbers has an upper bound, then it has a least upper bound. These two together define the real numbers completely in the context of the usual set theory, and allow its other properties to be deduced. For instance, we can prove from these properties that every polynomial of odd degree with real coefficients has a real root, and that if you add the square root of −1 to the real numbers, obtaining the complex numbers, the resulting field is algebraically closed.