Matemáticas | SELECTIVIDADFISICA.COM - Part 12

Examen Global1 1bto Ciencias19-20

10/12/2019 por rubensalvador

Examen Global1 1bto Ciencias19-20

Examen Global1 1bto CCSS 19-20

10/12/2019 por rubensalvador

Relación de derivadas 1º de Bachillerato

18/04/202005/04/2019 por rubensalvador

Derivadas sin regla cadena

24/03/202125/03/2019 por rubensalvador

DERIVADAS SIN NECESIDAD DE UTILIZAR LA REGLA DE LA CADENA

1– $f(x)=x^3-2x^2+3\sqrt{x}-4$

2– $f(x)=\sqrt[3]{x^2} - \frac{1}{x\sqrt[3]{x}}+\frac{3\sqrt[5]{x^2}}{x^2\sqrt{x}}$

3– $f(x)=\frac{2x^2}{x^2\sqrt{x^3}}-3x\sqrt[3]{x^2}+x^3\sqrt{x^4}$

4– $f(x)=\frac{x^2+2x-1}{2x^3+3}$

5– $f(x)=\frac{x\sqrt{x}}{x+\sqrt{x}}$

6– $f(x)=\frac{3x^3\sqrt[4]{x^2}}{\sqrt[5]{x^3}}$

7– $f(x)=x^3senx$

8– $f(x)=2senxcosx$

9– $f(x)=xlnx$

10– $f(x)=senxlnx$

11– $f(x)=x^2+tgx$

12– $f(x)=\frac{log_{3}x}{e^x}$

13–f(x)= $\frac{senxcosx}{x^2}$

14– $f(x)=\frac{xlnx+senx}{cosx}$

15– $f(x)=\frac{senxtagx}{x^2 2^x}$

16– f(x)= $\frac{x^22^x}{x^2+2^x}$

17– $f(x)=\frac{x^2tgx+lnxsenx}{x^2}$

18– $f(x)=\frac{xcosx}{tgx}$

19– $f(x)=\frac{1}{\sqrt[4]{x}}+x^3logx-\frac{1}{senx}$

20– $f(x)=\frac{3\sqrt[4]{x}cosx}{\sqrt[5]{x^3}}$

21– $f(x)=x^2e^x$

22– $f(x)=\frac{xsenx}{log_{7}x}$

23– $f(x)=e^{x} senx$

24– $f(x)= \frac{x^2+1}{x+1}$

25– $f(x)=xlnx$

26– $f(x)=\frac{x^2+1}{x-2}$

27– $f(x)=x^2 senx$

28– $f(x)=\frac{xcosx}{x+cosx}$

29– $f(x)=\frac{x-3}{x}$

30– $f(x)= \frac{tanx}{lnx}$

31– $f(x)=\frac{x^2+3}{senx}$

32– $f(x)=x^3 logx$

Explicación problema 18:

Explicación problemas 5, 6 y 15

Inecuaciones polinómicas y racionales

11/08/202017/12/2018 por rubensalvador

INECUACIONES POLINÓMICAS Y RACIONALES

1– $x^2 +x -2 \geq 0$

2– $x^2 -5x +4 < 0$

3– $x^2+x+2\geq 0$

4– $x^2+6x+9\leq 0$

5– $x^3 -2x^2 -5x +6 \geq 0$

6– $x^3 -8x^2 +20x -16 \leq 0$

8– $x^3 - 4x\geq 0$

9– $x^3 + 3x^2 - x< 0$

10– $-x^2+6x-8<0$

11– $-x^2 + 2x +3 <0$

12– $x^2 -x -2 <0$

13– $-x^2 + 4x -4 \leq 0$

15– $x^2 - 4 \geq 0$

16– $\frac{x+2}{x-3}<0$

17– $\frac{x}{x^2-4}\leq 0$

19– $\frac{x^2-2x+1}{x^2+x-6}\geq 0$

20– $\frac{x-2}{3-x} < 0$

21– $\frac{x^2+2}{x-3} \leq 0$

22– $\frac{x^2+x-6}{x^2-2x+1} \geq 0$

24– $\frac{x^2-1}{x^2-9} \leq 0$

25– $\frac{x^2-x}{x^2-4} \geq 0$

26– $\frac{(x+2)(x-3)^2}{5(x-1)} \geq 0$

Sistemas de ecuaciones lineales: método de Gauss

03/12/201917/12/2018 por rubensalvador

SISTEMAS LINEALES: MÉTODO DE GAUSS

1–

$\left.\begin{matrix} 3x+2y-z=3 \\ x+y-2z=-5\\ 2x+y+3z=16 \end{matrix}\right\}$

Sol: (1,2,4)

2–

$\left.\begin{matrix} 2x+y-3z=1 \\ x-2y+4z=19\\ 3x+4y-z=1 \end{matrix}\right\}$

Sol: (5,-3,2)

3–

$\left.\begin{matrix} x+y+z=2 \\ 2x-y+3z=11\\ x+2y-z=-2 \end{matrix}\right\}$

Sol: (3,-2,1)

4–

$\left.\begin{matrix} 2x-y+z=-8 \\ x+3y-2z=5\\ 2x+y+3z=4 \end{matrix}\right\}$

Sol: (-3,4,2)

5–

$\left.\begin{matrix} x+y-z=0 \\ 2x-3y+z=13\\ -3x+2y+5z=-8 \end{matrix}\right\}$

Sol: (3,-2,1)

6–

$\left.\begin{matrix} 2x-y+z=11 \\ x-y+3z=15\\ 3x+2y-5z=-17 \end{matrix}\right\}$

Sol: (2,-4,3)

7–

$\left.\begin{matrix} 4x-y-z=0 \\ 2x+y+z=3\\ 6x-2y-3z=-6 \end{matrix}\right\}$

Sol: (1/2, -3, 5)

8–

$\left.\begin{matrix} x+y+z=6 \\ 2x-y-3z=-9\\ 3x+y-2z=-1 \end{matrix}\right\}$

Sol: (1,2,3)

9–

$\left.\begin{matrix} 2x+y-2z=-10 \\ 3x-4y+5z=14\\ x+y-z=-4 \end{matrix}\right\}$

Sol: (-1,2,5)

10–

$\left.\begin{matrix} 2x-3y+z=10 \\ x+y-2z=-5\\ 5x-2y-2z=6 \end{matrix}\right\}$

Sol: (2,-1,3)

11–

$\left.\begin{matrix} 3x-2y-z=7 \\ 4x+y-2z=-5\\ 2x-3y-4z=-7 \end{matrix}\right\}$

Sol: (2,-3,5)

12–

$\left.\begin{matrix} \frac{x}{3}+\frac{y}{4}+z=\frac{17}{12} \\ \frac{x+y}{3}-\frac{z}{2}=-\frac{1}{6}\\ \frac{x}{2}-\frac{y+z}{6}=1 \end{matrix}\right\}$

Sol: (2,-1,1)

13–

$\left.\begin{matrix} x+y+z=18 \\ \frac{x}{3}=\frac{y}{4} \\ \frac{x}{3}=\frac{z}{5} \end{matrix}\right\}$

Sol: (9/2, 6, 15/2)

14–

$\left.\begin{matrix} x+2y-3z=7\\ 2x+y-z=6 \\ 3x-y-z=6 \end{matrix}\right\}$

Sol: (2,1,-1)

15–

$\left.\begin{matrix} x+y-z=5\\ 2x-3y-z=3 \\ 3x-2y-2z=5 \end{matrix}\right\}$

Sol: Incompatible

16–

$\left.\begin{matrix} 2x+y+z=5\\ 2x-y+3z=3 \\ 3x+2y+z=8 \end{matrix}\right\}$

Sol: Compatible indeterminado (2-z, 1+z, z)

17–

$\left.\begin{matrix} x+2y-2z=2\\ 3x-3y+z=-14 \\ 5x-y-2z=-15 \end{matrix}\right\}$

Sol: (-2,3,1)

18–

$\left.\begin{matrix} 2x+4y-z=0\\ 3x-3y-2z=-1 \\ 3x-3y+2z=5 \end{matrix}\right\}$

Sol: (25/36 , 1/36 , 3/2)

19– $\left.\begin{matrix} 2x+y-z=11\\ 2x-2y-z=8 \\ x+y-z=7 \end{matrix}\right\}$

20– $\left.\begin{matrix} 4x+y-5z=5\\ 5x-y-z=13\\ 4x-2y-3z=14 \end{matrix}\right\}$

21– $\left.\begin{matrix} x+y-2z=0\\ 2x-3y+3z=4\\ 5x-5y+4z=8 \end{matrix}\right\}$

22– $\left.\begin{matrix} 5x+2y-2z=0\\ 3x-y+3z=0\\ 8x+y+z=-1 \end{matrix}\right\}$

23– $\left.\begin{matrix} x+3y-2z=0\\ x-y+3z=0\\ 2x+2y+z=0 \end{matrix}\right\}$

24– $\left.\begin{matrix} 2y-z=-1\\ 5x-y-3z=2\\ x-y+2z=-2 \end{matrix}\right\}$

25– $\left.\begin{matrix} x-y+z=10\\ 4x+2y+c=-8\\ 9x+3y+z=-22 \end{matrix}\right\}$

26– $\left.\begin{matrix} x+3y-2z=6\\ 2x+3y-2z=8\\ 4x+2y-6z=6 \end{matrix}\right\}$

27– $\left.\begin{matrix} x+2y-3z=3\\ 3x-2y+z=7\\ 5x+2y-5z=1 \end{matrix}\right\}$

28– $\left.\begin{matrix} 2x+y-2z=8\\ 2x-4y+3z=-2\\ 4x-y+6z=-4 \end{matrix}\right\}$

29– $\left.\begin{matrix} x+3y-2z=-6\\ 2x-3y+5z=6\\ 5x-3y+8z=6 \end{matrix}\right\}$

30– $\left.\begin{matrix} x+2y-2z=4\\ 2x+5y-2z=10\\ 4x+9y-6z=18 \end{matrix}\right\}$

31– $\left.\begin{matrix} x+2y-z=-5\\ 5x-y+2z=11\\ 6x+y+z=5 \end{matrix}\right\}$

32– $\left.\begin{matrix} 2x+y+z=0\\ 3x+2y-2z=15\\ x+y-z=7 \end{matrix}\right\}$

33– $\left.\begin{matrix} x+3y-2z=4\\ 2x+2y+z=3\\ 3x+2y+z=5 \end{matrix}\right\}$

34– $\left.\begin{matrix} x+3y-2z+2w=12 \\ 2x-2y-z+w=5 \\ 3x+y-2z-4w=16 \\ 3x-3z-3w=15 \end{matrix}\right\}$

Sistemas de ecuaciones no lineales , exponenciales y logarítmicas

29/10/202416/12/2018 por rubensalvador

SISTEMAS DE ECUACIONES NO LINEALES / EXPONENCIALES / LOGARÍTMICAS

1– $\left.\begin{matrix} x^2 +y^2=25 \\ x-y=1 \end{matrix}\right\}$ Sol: (0,-1) y ( $\frac{25}{313}$ , $\frac{312}{313}$ )

2– $\left.\begin{matrix} x-2y=0 \\ x^2+y^2=20 \end{matrix}\right\}$ Sol : (-4, -2) y (4,2)

3– $\left.\begin{matrix} 2x+y=2 \\ y=x^2-3x-4 \end{matrix}\right\}$ Sol : (-2,6) y (3,-4)

4– $\left.\begin{matrix} 5x-y=3 \\ 5x^2-y=13 \end{matrix}\right\}$ Sol: (-1, -8) y (2,7)

5– $\left.\begin{matrix} y=\frac{6}{x} \\ 2y=3x \end{matrix}\right\}$ Sol : (-2,-3) y (2,3)

6– $\left.\begin{matrix} x+y=5 \\ x^2-y^2=9 \end{matrix}\right\}$ Sol : (17/5 , 8/5)

7– $\left.\begin{matrix} \frac{4}{3}x+y=\frac{25}{3} \\ x^2+y^2=25 \end{matrix}\right\}$ Sol: (4,3)

8– $\left.\begin{matrix} 8x-y^2=0 \\ 2x-y=8 \end{matrix}\right\}$

Sol: (2, -4) y (8,8)

9– $\left.\begin{matrix} y=\frac{6}{x}\\ x^2+y^2=13 \end{matrix}\right\}$ Sol: (-3, -2) , (-2, -3) , (3,2) y (2,3)

10– $\left.\begin{matrix} 4x=y^2\\ 2x-y=-2 \end{matrix}\right\}$ Sol: No existe

11– $\left.\begin{matrix} x+2y=\frac{3}{x}\\ x+y=\frac{2}{y} \end{matrix}\right\}$ Sol : (-1 , -1) y (1 , 1)

12– $\left.\begin{matrix} 3^x+5^y=14\\ 4\cdot 3^x-7\cdot 5^y=1 \end{matrix}\right\}$ Sol: (2,1)

13– $\left.\begin{matrix} logx +2logy=log2+log9\\ logx-logy=log2-log3 \end{matrix}\right\}$ Sol (2,3)

14– $\left.\begin{matrix} 2^x+3^y=11\\ 2^{x+1}-3^{y-1}=1 \end{matrix}\right\}$ Sol: (1,2)

15– $\left.\begin{matrix} 2logx+logy=2\\ logxy=1 \end{matrix}\right\}$ Sol: (10,1)

16– $\left.\begin{matrix} x-y=2\\ 5\cdot 2^x-2\cdot 4^{y+1}=8 \end{matrix}\right\}$ Sol: (1,-1) y (3 , 1)

17– $\left.\begin{matrix} x+y=11\\ logx=logy+1 \end{matrix}\right\}$

18– $\left.\begin{matrix} 5^x=25\cdot 5^y\\ log(x+y)-log(x-y)=log2 \end{matrix}\right\}$

19– $\left.\begin{matrix} 4\cdot 2^x=4^{y+1}\\ log(x+y)+log(x-y)=log3 \end{matrix}\right\}$

20– $\left.\begin{matrix} 2x+y=8\\ 2x+3y^2=22 \end{matrix}\right\}$

21– $\left.\begin{matrix} 2x+5y=-8\\ xy-3x=-5 \end{matrix}\right\}$

22– $\left.\begin{matrix} x+y=0\\ xy=1 \end{matrix}\right\}$

23– $\left.\begin{matrix} 2x-y=3\\ x^2-y^2=3 \end{matrix}\right\}$

24– $\left.\begin{matrix} 2x^2+3y^2=32\\ -3x^2+4y^2=-48 \end{matrix}\right\}$

25– $\left.\begin{matrix} xy=-3\\ x^2+2y^2=19 \end{matrix}\right\}$

26– $\left.\begin{matrix} \frac{x-2y}{x+2y}+\frac{x+2y}{x-2y}=\frac{10}{3}\\ x+3y=7 \end{matrix}\right\}$

27– $\left.\begin{matrix} \ x-6y=-6\\ 2x^2+y^2=76 \end{matrix}\right\}$

28– $\left.\begin{matrix} \ 3xy-2x^2=-26\\ 4x+5y=-7 \end{matrix}\right\}$

29– $\left.\begin{matrix} \ 3x+\frac{y}{2}=15\\ \frac{2}{x}+\frac{3}{y}=1 \end{matrix}\right\}$

30– $\left.\begin{matrix} \ 2x+4y=10\\ \ x^2+3xy=-8 \end{matrix}\right\}$

31– $\left.\begin{matrix} \ 3x^2+5y^2=20\\ \ 4x^2-y^2=-4 \end{matrix}\right\}$

32– $\left.\begin{matrix} \ x^2-2(x-y)^2=36\\ \ \frac{x}{2}+\frac{y}{3}=5 \end{matrix}\right\}$

33– $\left.\begin{matrix} \ \frac{x}{y}=\frac{x-1}{1-y}\\ \ xy=1 \end{matrix}\right\}$

34– $\left.\begin{matrix} \ 2logx-3logy=7\\ \ logx+logy=1 \end{matrix}\right\}$

35– $\left.\begin{matrix} \ x-y=21\\ \ logx+logy=2 \end{matrix}\right\}$

36– $\left.\begin{matrix} \ 2^x+5^y=9\\ \ 2^{x+2}+5^{y+1}=4 \end{matrix}\right\}$

37– $\left.\begin{matrix} \ 3^x+7^y=16\\ \ 3^{x-1}-7^{y+2}=-340 \end{matrix}\right\}$

38– $\left.\begin{matrix} \ logx+3logy=5\\ \ logx-logy=3 \end{matrix}\right\}$

39– $\left.\begin{matrix} \ 3x+2y=64\\ \ logx-logy=1 \end{matrix}\right\}$

40– $\left.\begin{matrix} \ 2^x+3^y=11\\ \ 4^x+9^y=85 \end{matrix}\right\}$

41– $\left.\begin{matrix} \ 15\cdot 5^x-6^{y+1}=339\\ \ 3\cdot 5^{x+1}+2\cdot 6^{y+2}=807 \end{matrix}\right\}$

42– $\left.\begin{matrix} \ 2^x+2\cdot 3^{y+1}=8\\ \ 5\cdot 2^{x-1}+9^y=6 \end{matrix}\right\}$

43– $\left.\begin{matrix} \ 3^x+3^{y+1}=18\\ \ x-3y=-1 \end{matrix}\right\}$

44– $\left.\begin{matrix} \ x+y=33\\ \ logx-logy=1 \end{matrix}\right\}$

45– $\left.\begin{matrix} \ logx^2-logy^2=2\\ \ x^2+y^2=29 \end{matrix}\right\}$

46– $\left.\begin{matrix} \ logx-logy=1\\ \ 2+logy-logx=log250 \end{matrix}\right\}$

47– $\left.\begin{matrix} \ 2log(x-2)+3log(y+2)=2\\ \ 4log(x-2)+5log(y+2)=-1 \end{matrix}\right\}$

48– $\left.\begin{matrix} \ logx-logy=1\\ \ 2^{x-24}=4^y \end{matrix}\right\}$

49– $\left.\begin{matrix} \ 4^x+3\cdot 2^y-40=0\\ \ 2^{x+y}=32 \end{matrix}\right\}$

Ecuaciones logarítmicas

29/10/201916/12/2018 por rubensalvador

ECUACIONES LOGARÍTMICAS

1– $log (2x+3)-logx=1$

2– $log(x+3)+logx=1$

3– $4logx+1=log16+log5x$

4– $log(x+3)-log(x-2)+2log5=2$

5– $log_{3}(5x+2)-log_{3}(2x-1)=1$

6– $lnx+ln(x+1)-ln2=ln3$

7– $log_{2}(2x+5)-log_{2}(x)+log_{2}3=log_{2}11$

8– $\frac{1}{2}log(x-16)=log3$

9– $log3x=log6+2logx$

10– $log(2x+3)-log(x-2)=2log2+2log3$

11– $log(\frac{2x-2}{x})=2log(x-1)-logx$

12– $log(4-5x)+log(2x-2)=log(2x-x^2)+1$

13– $5logx=3logx+2log6$

14– $log(3x^2+5x+30)-log(3x+8)=1$

15– $\frac{logx}{2}=\frac{1}{2}+log\sqrt{2}$

16– $2log(2x-2)-log(x-1)=1$

17– $log(65-x^3)=3log(5-x)$

18– $logx=log6+2log\frac{x}{3}$

19– $log10^{\sqrt{20x+320}}=10\sqrt{x}$

20– $3log_{x}2+log_{x}4=-5$

21– $log\sqrt{7x+51}-1=log9-log\sqrt{2x+67}$

Ecuaciones exponenciales

18/12/201916/12/2018 por rubensalvador

ECUACIONES EXPONENCIALES

1– $3^{x+2}+3^{x}=90$

2– $4^{x}-7\cdot 2^{x}-8 =0$

3– $7^{x-1}-2^{x}=0$

4– $2^{x}+2^{x+1}=24$

5– $9^{x}-10\cdot 3^{x}+9=0$

6– $5^{x+2}-3^{x+1}=0$

7– $4^{x}-10\cdot 2^{x}+16=0$

8– $5^{x-1}+5^{x}+5^{x+1}=31$

9– $6^{x-3}-5^{x+4}=0$

10– $3^{x}+3^{x+1}=12$

11– $2^{x+1}=3^{x-1}$

12– $3^{x+2}-4^{x-3}=0$

13– $5^{x+2}-4\cdot 5^{x+1}-8\cdot 5^{x-1}=85$

14– $4\cdot 2^{2x}-33\cdot 2^{x}+8=0$

15– $3\cdot 3^{2x}-28\cdot 3^{x}+9=0$

16– $2^{x-2}+2^{x-1}+2^{x}+2^{x+1}=30$

17– $5^{x-2}-4^{x+1}=0$

18– $4^{x+1}-7^{x-1}=0$

19– $3^{x-1}+3^{x}+3^{x+1}=39$

20– $5^{2x}-6\cdot 5^{x}+5=0$

21– $3^{x^{2}-x-6}=1$

22– $2^{1-x^{2}}=\frac{1}{8}$

23– $3^{5x-4}=9^{2x-1}$

24– $2^{x}=\sqrt[3]{4}$

25– $0,5^{x}=32$

26– $\sqrt[5]{7^{x}}=23$

27– $\frac{1}{9^{x}}=27$

28– $\frac{1}{2^x}=16^{\frac{x(x-1)}{2}}$

29– $3\cdot 2^x=2\cdot 3^x$

30– $13^{x^2+2x}-\frac{1}{13}=0$

31– $2^{2x^2-3x-5}=16$

32– $2^{x-1}+2^x+2^{x+1}=7$

33– $2^{x+4}-8^x=0$

34– $3^{2x}-3^{x-1}=3^{x+1}-1$

35– $5^{x+3}-5^{x-1}-3120=0$

36– $5^{2x}-30\cdot 5^x+125=0$

37– $2\cdot 10^{2x+4}+3\cdot 10^{x+2}-5=0$

38– $4^{x^2+1}=2^{5x+5}$

39– $4^{(x-2)^2}=262144$

40– $9^x+5\cdot 3^x-24=0$

41– $3^{x+2}+9^{x-1}=90$

42– $3^{2x}+3^{2x-1}+3^{x-1}=111$

43– $2^{2x-4}-5\cdot 2^{x-3}+1=0$

44– $9^{x+2}+3^{x+3}-810=0$

45– $\sqrt[x]{27}=3^{x+2}$

Ecuaciones irracionales

22/10/202415/12/2018 por rubensalvador

ECUACIONES IRRACIONALES

1— $5+\sqrt{3x+7}=x+6$

2– $3x+\sqrt{17-4x}= 4x+1$

3– $3-x+\sqrt{3x+12}=x+8$

4– $\sqrt{2x+6}-\sqrt{x-1}=2$

5– $\sqrt{5x+1}=5-\sqrt{x-2}$

6– $12 + \sqrt{3x+10}=2x+7$

7– $\sqrt{x+6}+4=6+\sqrt{2x-5}$

8– $5x-\sqrt{x+2}=3x+2$

9– $\sqrt{x+9}+\sqrt{x}=9$

10–

11– $x+\sqrt{2x^2 +2x-3}=-1$

12– $\sqrt{3\sqrt{16-x}}=\sqrt{2x-5}$

13– $\frac{x-1}{\sqrt{x}}=x-\frac{5}{2}$

14– $\sqrt{x+4}+\sqrt{x-1}=5$

15– $\sqrt{x-7}+\sqrt{2x}=\sqrt{x+1}$

16– $2-3\sqrt{x}=-x$

17– $3x+\sqrt{2x-2}=2\sqrt{2x-2}+23$

18– $\sqrt{x+1}+\sqrt{2x+3}=5$

19– $3\sqrt{3x-1}=2\sqrt{3(2x-1)}$

20– $\sqrt{x+5}+\sqrt{x}=\sqrt{7x-3}$

21– $\frac{2\sqrt{x}}{4+\sqrt{x-5}}=\frac{4-\sqrt{x-5}}{\sqrt{x-5}}$

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