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(Solved): (1) \int_0^((1)/(2)ln(5)) e^(x)= (A) \sqrt(3) B) \sqrt(3)-1 C) \sqrt(5) (2) The graph of the functio ...



(1)

\int_0^((1)/(2)ln(5)) e^(x)=

(A)

\sqrt(3)

B)

\sqrt(3)-1

C)

\sqrt(5)

(2) The graph of the function

f(x)=(lnx)/(x)

has a relative maximum at

x=

(A)

e

D)

\sqrt(5)-1

(3) From the accompanying figure, the graph of

y=f(x)

is increasing on: A)

(-\infty ,+\infty )

B)

(-\infty ,0]

C)

[0,+\infty )

D)

-1,1

(4) If

f(x)=x^(5)+x^(3)+x

, then

(f^(-1))^(')(0)=

A)

(1)/(3)

B) 3 C) 1 D)

(1)/(9)

(5)

(d)/(dx)[tan^(-1)(x^(3))]=

A)

(3x^(2))/(1+x^(6))

B)

(2x)/(1+x^(4))

C)

(x^(2))/(1+x^(6))

D)

(x)/(1+x^(4))

(6)

sin[2cos^(-1)((3)/(5))]=

A)

(\sqrt(3))/(2)

B)

(24)/(25)

C)

(\sqrt(3))/(4)

D)

(24)/(5)

(7) The domain of the function

y=ln(x^(2)-4x+4)

is: A)

(-\infty ,-2)\cup (2,+\infty )

B)

(-2,2)

C)

(-\infty ,2)\cup (2,+\infty )

D)

(2,+\infty )

(8) The value of

x

such that

3^(x)=2^(x+1)

is: A)

(ln(2))/(ln(3)-ln(2))

B)

ln((2)/(3))

C)

ln((3)/(2))

D)

ln(3)-ln(2)

(9)

\lim_(x->+\infty )(1+(9)/(x))^(5x)=

: A) 1 B) 0 C)

e^(45)

D)

e^((5)/(9))

(10) Let

F(x)=\int_0^x (sint)/(t^(2)+1)dt

. Find

F^(')(0)

; A)

\pi

B) 0 C)

(1)/(2)

D) 1



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