$f\left( x \right) = y$ va ${x^2} - 2x = {e^{x - y}}$ bo‘lsa, $f'\left( 4 \right)$ ning qiymatini toping.

$4{x^2} + \frac{1}{{{x^2} - 4}} = 16 - \frac{1}{{4 - {x^2}}}$ tenglamani yeching.

$n - \;$hadi ${a_n}$ bo‘lgan arifmetik progressiya uchun ${a_n} = 2 + {a_{n - 1}}$ tenglik o‘rinli bo‘lib, dastlabki o‘nta hadining yig‘indisi $115$ ga teng bo‘lsa, arifmetik progressiyaning birinchi hadini toping.

$\frac{{1 + 3 + 5 + \ldots + 43}}{{2 + 4 + 6 + \ldots + 42}}$ ni hisoblang.

Ishlab chiqarish samaradorligi birinchi yili $15\%$ ga, ikkinchi yili $16\%$ ga ortdi. Shu ikki yil ichida samaradorlik necha $\%$ ga ortgan?

$\;\left( {x - 5} \right) \cdot \left( {\frac{1}{5}x + 4} \right) = 0$ bo‘lsa, $\frac{1}{5}x + 4$ qanday qiymatlar qabul qiladi?

$f\left( x \right) = \left| {\left| {x - 2} \right| - 2} \right|$ funksiya grafigini chizing.

Quyidagi rasmda qirrasining uzunligi $6\;{\rm{sm}}$ bo‘lgan muntazam tetraedr tasvirlangan:

Agar $BD = FE = 4\;{\rm{sm}};{\rm{\;\;}}DC = AF = 2\;{\rm{sm}}$ va $O$ nuqta $AC$ qirrada ekanligi ma’lum bo‘lsa, $DO + OF$ yig‘indining eng kichik qiymatini $\left( {{\rm{sm}}} \right)$ toping.

$n + 7$ soni juft son bo‘lsa, quyidagilardan qaysi biri toq son bo‘ladi?

Muntazam oltiburchakka tashqi chizilgan aylananing radiusi $4\sqrt 3$ ${\rm{sm}}\;$ga teng bo‘lsa, uning kichik diagonalini $\left( {{\rm{sm}}} \right)$ toping.

$\;\left( {e - \pi } \right)x \ge 7\left( {\pi - e} \right)$ tengsizlikni yeching.

${9^{{x^2} - 1}} + {3^{{x^2}}} - 4 = 0$ tenglamaning butun ildizlari yig‘indisini toping.

${\left( {2{x^2} - \frac{1}{{{x^2}}}} \right)^7} = \ldots + p \cdot {x^6} + \ldots$ bo‘lsa, $p$ ning qiymatini toping.

Teng yonli $ABCD$ trapetsiyaning ichida $P$ nuqta shunday olinganki, $PA = 2;\;\;PB = 3;\;\;PC = 4$ va $PD = 5$ ga teng. Agar $AD$ katta asos bo’lsa, $\frac{{BC}}{{AD}}$ ning qiymatini toping.

$f\left( x \right) = f\left( 5 \right) \cdot x - 20$ bo‘lsa, $f\left( 4 \right)$ ning qiymatini toping.

$f\left( {\frac{{3x - 1}}{{x + 2}}} \right) = \frac{{x + 1}}{{x - 1}}$ bo‘lsa, $f\left( x \right)$ ni toping.

Quyidagi rasmda ko‘rsatilgan krandan konus ichiga doimiy bir xil suv oqib tushadi.

Agar kran konusni bo‘yalgan qismini $4$ minutda to‘ldirsa, butun konusni necha minutda to‘ldiradi?

Quyidagi rasmda tasvirlangan $ABC$ uchburchakning tomonlarida $9$ ta nuqta olingan:

Uchlari ko‘rsatilgan nuqtalarda bo‘lgan nechta uchburchak bor?

$\;\frac{{10!}}{{7!}} \cdot \left( {\frac{{8!}}{{10!}} + \frac{{3!}}{{5!}}} \right)$ ni hisoblang.

$P\left( x \right) = {\left( {x - 1} \right)^a} \cdot {\left( {x + 2} \right)^b}$ va $P\left( 2 \right) \cdot P\left( 1 \right) = 64$ bo‘lsa, $a + b$ ning qiymatini toping.

$32;\;\;18$ va $24$ sonlarining o‘rta geometrigini toping.

Quyidagi rasmda $y = f\left( x \right)$ funksiya grafigi tasvirlangan:

Rasmda berilgan ma’lumotlardan foydalanib, $\left( {x - 3} \right) \cdot f\left( x \right) > 0$ tengsizlikni qanoatlantiradigan butun sonlar yig‘indisini toping.

Sardor $420$ ${\rm{m}}$ masofani $7$ ${\rm{daqiqa}}$da bosib o‘tadi. Sardorning tezligini $\left( {{\rm{m}}/{\rm{min}}} \right)$ toping.

${\left( {\sqrt {6 + \sqrt {35} } } \right)^x} + {\left( {\sqrt {6 - \sqrt {35} } } \right)^x} = 12$ tenglamaning butun ildizlari ko‘paytmasini toping.

${\left( {{4^{\frac{{{{\log }_4}7}}{{{{\log }_7}4}}}} - {7^{{{\log }_4}7}} + {3^{{{\log }_9}16}}} \right)^{\frac{1}{2}}}$ ni hisoblang.

Aniq integralni hisoblang:
$\mathop \smallint \nolimits_0^3 \frac{x}{{\sqrt {1 + {x^2}} }}dx + \mathop \smallint \nolimits_0^3 \frac{1}{3}dx$

Quyidagi chizmada berilgan ma’lumotlardan foydalanib, $x\;$ni toping.

$\frac{{{{\left( {2\left| x \right| - 3} \right)}^2} - \left| x \right| - 6}}{{4x + 1}} = 0$ tenglamaning haqiqiy ildizlari yig‘indisini toping.

$\cos 3x - \sqrt 3 \sin 3x < 0$ tengsizlikni yeching.

Soddalashtiring: $\frac{{{{\left( {a + 1} \right)}^3} + 1}}{{{a^3} - 1}}$