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1.

con base en

\int_0^1\int_1^2\left(4x^3-9x^2y^2dy\right)dx

indica el resultado de la integración inicial con respecto a y

a)

$4x^3-21x^2$

b)

$4x^3+21x^2$

c)

$4x^3-63x^2$

2.

$\int_{-1}^2\int_x^{3x}dydx$

a)

1

b)

3

c)

-3

d)

-1

3.

La integral de $\int_{ }^{ }\frac{1}{2x+1}dx$ es

a)

$\ln\left|2x+1\right|+C$

b)

$\frac{1}{2}\ln\left|2x+1\right|+C$

c)

$2\ln\left|2x+1\right|+C$

d)

$\frac{1}{2x+1}+C$

4.

$\int_{ }^{ }\tan\left(x\right)dx$

a)

$-\ln\left|\cos\left(x\right)\right|+c$

b)

$\ln\left|\cos\left(x\right)\right|+c$

c)

$\ln\left|sen\left(x\right)\right|dx$

d)

$-\ln\left|sen\left(x\right)\right|dx$

5.

$\int_{ }^{ }\ 18\sqrt{x}\ dx=$

a)

$27\sqrt{x^3}+c$

b)

$-12x^{-\frac{1}{2}}+c$

c)

$12x^{-\frac{1}{2}}+c$

d)

$12\sqrt{x^3}+c$

6.

Sea la función

z=e^{x-3y}

donde

x=vu^3-v

como

y=u-4v

las derivadas

\frac{\partial z}{\partial u}

y

\frac{\partial z}{\partial v}

es:

a)

$\frac{\partial z}{\partial u}=3e^{x-3y}\left(vu^2-1\right);\ \frac{\partial z}{\partial v}=e^{x-3y}\left(u^3+11\right)$

b)

$\frac{\partial z}{\partial u}=3e^{x-3y}\left(u^3+11\right);\ \frac{\partial z}{\partial v}=e^{x-3y}\left(vu^2-1\right)$

c)

$\frac{\partial z}{\partial u}=3e^{x-3y}\left(u^3-11\right);\ \frac{\partial z}{\partial v}=e^{x-3y}\left(vu^2+1\right)$

7.

Si $f\left(x\right)=\sqrt{1-x^2}$ , entonces $f'\left(x\right)=\frac{\left[\ \ \right]}{2\sqrt{1-x^2}}$

(a)

8.

Sea la función

f=x+\left(y-2\right)^3

donde

x=r+5t

como

y=3r-4t

la derivada

\frac{\partial f}{\partial t}

es:

a)

$\frac{\partial f}{\partial t}=5-12\left(y-2\right)^2$

b)

$\frac{\partial f}{\partial t}=5+12\left(y-2\right)^2$

c)

$\frac{\partial f}{\partial t}=5-12\left(y+2\right)^2$

d)

$\frac{\partial f}{\partial t}=5+12\left(y+2\right)^2$

9.

Hallar la derivada de $f\left(x\right)=\left(3x^2-5x\right)^3$

a)

$(18x−15)^2(3x^2−5x)^2$

b)

$\left(18x-15\right)\left(3x^2-5x\right)^2$

c)

$(18x−15)(3x^2−5x)^3$

d)

$(18x−15)(3x−5)^2$

10.

Hallar la derivada de $y=\left(x+3\right)^2$

a)

$2x$

b)

$2\left(x+3\right)^2$

c)

$2x+6$

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Total questions: 10

Worksheet time: 18mins

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