Processing math: 17%




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16.

 The integral  (1+x1x)ex+1xdx  id equal to 


A) (x1)ex+1/x+C

B) xex+1/x+C

C) (x+1)ex+1/x+C

D) xex+1/x+C



17.

If x=-1 and x=2  are extreme points of   f(x)=\alpha\log|x|+\beta x^{2}+x , then


A) \alpha=-6,\beta=\frac{1}{2}

B) \alpha=-6,\beta=-\frac{1}{2}

C) \alpha=2,\beta=-\frac{1}{2}

D) \alpha=2,\beta=\frac{1}{2}



18.

 If f and g are differentiable functions in (0,1)  satisfying f(0)=2=g(1), g(0)=0  and f(1)=6 , then for some c ε ]0,1[


A) 2f'(c)=g'(c)

B) 2f'(c)=3g'(c)

C) f'(c)=g'(c)

D) f'(c)=2g'(c)



19.

 If g is the inverse of  a function f and   f'(x)=\frac{1}{1+x^{5}}  , then g'(x) is equal to


A) 1+x^{5}

B) 5x^{4}

C) \frac{1}{1+\left\{g(x)\right\}^{5}}

D) 1+{g(x)}^{5}



20.

\lim_{x \rightarrow 0}\frac{\sin(\pi\cos^{2}x)}{x^{2}}   is equal to 


A) \frac{\pi}{2}

B) 1

C) \pi

D) -\pi



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