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>07.04.07

TEST! (32p.)

2rr + arctan(n)    Łn^Z + 5

w    —    *

^tr & + <±r^ci'°“h

c) lim

l.(4p.+4p.+4p.+4p.) Find the following limits (do not use derivatives):

-

x~* 0⁺ sin(x²) y--p O x^j/

A' O- O

2. (4p.+4p.) Classify the follcwmg-series-n

»>X

3 w!

jg (" + D"

3. (4p.) Show that the following limit does not exist

Ikn. x vtah(x) -

yhr 1 < x £ 3 for x'Ł'*>

SU-.TT

yv\

jU>* 4Lto X-⁵? 4*"

^__' •>

4. (4p.) Find the values of a € *, b e R for which the following function /:*->* ¹⁵

continuous

a • arcsin(2x² -1) for xś 1

IB

ln(—)

x²-9

" x²/9> + 6

-jloAł?

-n Osf /i aO. fiU) CQV1L-V5 K C^f

€.(enr»€ł^*^ (\t^\cłCo* -    ⁵⁰

(X> tr(j\! »uuix> u s .

I o 7    - Ok o-rr ^

<0    cl»

*1^ . 4®.*

(Ufo-e) _£l:³^

-a,'    H

fo)    ^(J*) - 1*; tJ; i

|||| ^Ł

*> (t> - 7