Category: Calculus

There will 5-7 math question. I need to it to be done with it showing every step hand written on piece of paper. It needs to shown work for every step of the way.

Calculs is very important topic in students list for math but my notes is very interesting.

Best concept for students easy concept

sin^2x+cos^2x = 1

Integration of e^x[(1-x)/(1+x^2)] dx =__________+ C.

A) e^x/(1+x^2)

B) e^x/(1+x^2)^2

C) -e^x/(1+x^2)

D) e^x/(1+x)

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y = 3secx + logx + 4

integration 1/x dx

1. Ce este delta ()?

Delta apare la ecuaiile de gradul al doilea, adic de forma:

ax^2 + bx + c = 0

unde:

• a 0
• a, b, c sunt numere reale

2. Formula pentru delta

Aici intervine delta:

Delta = b^2 – 4ac

3. Cum interpretm delta?

Dup ce calculezi , ai 3 cazuri:

• > 0 2 soluii reale diferite
• = 0 1 soluie (dubl)
• < 0 nu exist soluii reale

4. Formula soluiilor

Dac 0, soluiile sunt:

x_{1,2} = frac{-b pm sqrt{Delta}}{2a}

5. Exemplu rezolvat

Rezolvm ecuaia:

x^2 – 5x + 6 = 0

Pasul 1: Identificm coeficienii

• a = 1
• b = -5
• c = 6

Pasul 2: Calculm delta

Delta = (-5)^2 – 4 cdot 1 cdot 6

Delta = 25 – 24 = 1

Pasul 3: Calculm soluiile

x_{1,2} = frac{-(-5) pm sqrt{1}}{2 cdot 1}

x_{1,2} = frac{5 pm 1}{2}

Pasul 4: Rezultatul final

• x_1 = frac{5 + 1}{2} = 3
• x_2 = frac{5 – 1}{2} = 2

Rspuns:

Soluiile sunt x = 3 i x = 2

Mic truc de reinut:

Dac poi descompune ecuaia (ex: (x-2)(x-3)=0), ajungi mai rapid la rezultat dar delta merge mereu, chiar i cnd nu se vede descompunerea.

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