\(f\left( x \right) = {3^x} \cdot {\rm{tg}}x\) bo’lsa, \(f'\left( 0 \right)\) ning qiymatini toping.

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

\(\mathop \smallint \nolimits_{ - 4}^{ - 3} f\left( x \right)dx = 2\;\)
va\(\;{S_3} - {S_2} = 2\) bo‘lsa,
\(\mathop \smallint \nolimits_{ - 2}^{ - 4} f\left( x \right)dx\)
ning qiymatini toping.

\(\overline {ab} + \overline {bc} + \overline {ca} = \overline {abc} \) bo‘lsa, \(a \cdot b \cdot c\) ning qiymatini toping.

\(x \ne 10\) va \(f\left( x \right) = \sqrt[3]{{x\left( {20 - x} \right)}}\) bo‘lsa, \(\frac{{f\left( {10 - x} \right)}}{{f\left( {10 + x} \right)}}\) ning qiymatini toping.

\(y = 8x + 19\) funksiyani \(\vec m\left( {6;3} \right)\) vektor bo‘yicha parallel ko‘chirsak, qanday funksiya hosil bo‘ladi?

\(f\left( x \right) = {\left( {5{x^3} - 1} \right)^{2017}} \cdot {\left( {2016{x^7} + 1} \right)^5} + {x^{37}} + 14\) ko’phadning ozod hadini toping.

\(ABCD\) parallelogrammning tomonlari \(AB = 25\;{\rm{sm}}\) va \(BC = 34\;{\rm{sm}}\) ga teng. \(DC\) tomonga \(BH\) balandlik tushirilgan hamda \(BC\) tomondan \(M\) va \(AD\) tomondan \(N\) nuqta olingan. \(MN\) kesma \(AD\) tomonga perpendikulyar va \(BH\) ni \(K\) nuqtada kesib o‘tadi. Agar \(MN = \frac{{375}}{{11}}\;{\rm{sm}}\) va \(BK = KH\) bo‘lsa, \(AK\) kesma uzunligini \(\left( {{\rm{sm}}} \right)\) toping.

\(1 \cdot 2 \cdot 3 \cdot \ldots \cdot 54 \cdot 55\) ko‘paytma nechta nol bilan tugaydi?

\(\frac{{{7^x} + 7}}{{{7^x} - 7}} + \frac{{{7^x} - 7}}{{{7^x} + 7}} \ge \frac{{4 \cdot {7^x} + 96}}{{{{49}^x} - 49}}\) tengsizlikni yeching.

\(f\left( x \right) = {\rm{lo}}{{\rm{g}}_2}\left( {x + \sqrt {1 + {x^2}} } \right)\) funksiya uchun quyidagilardan qaysi biri to‘g‘ri?

\(f\left( {{\rm{sin}}x} \right) + f\left( {{\rm{cos}}x} \right) = 3\) bo‘lsa, \(f\left( x \right)\) ni toping.

\({2222^{5555}} + {5555^{2222}}\) sonini \(7\) ga bo‘lgandagi qoldiqni toping.

Quyidagi rasmda ko‘rsatilgan ma’lumotlardan foydalanib, \(x\) ning qiymatini toping.

Formula \(3\) ta kitob ichidan qidirilyapti. Formulaning birinchi kitobdan topilish ehtimoli \(0,6\) ga, ikkichi kitobdan topilish ehtimoli \(0,7\) ga, uchinchi kitobdan topilish ehtimoli \(0,8\) ga teng bo‘lsa, formulaning faqat \(2\) ta kitobdan topilish ehtimolini toping.

\(5\sqrt 2 \sin \frac{{3\pi }}{8}\cos \frac{{3\pi }}{8}\) ning qiymatini toping.

Quyidagi rasmda \(f\left( x \right) = {a^x}\) funksiya grafigi tasvirlangan:

Rasmda berilgan ma’lumotlardan foydalanib, \(f\left( 4 \right)\) ning qiymatini toping.

\(\frac{1}{{x\left( {x + 1} \right)}} + \frac{1}{{\left( {x + 1} \right)\left( {x + 2} \right)}} + \frac{1}{{\left( {x + 2} \right)\left( {x + 3} \right)}} + \frac{1}{{\left( {x + 3} \right)\left( {x + 4} \right)}} + \frac{1}{{\left( {x + 4} \right)\left( {x + 5} \right)}}{\rm{\;}}\)ni soddalashtiring.\({\rm{\;}}\)

\(\vec a\left( {3;\;7} \right)\) va \(\vec b\left( {8;9} \right)\) bo‘lsa, \(1,2\vec a - 0,7\vec b\) vektorning uzunligini toping.

\({6^{46}}:23 = A\;\left( q \right)\) bo‘lsa, \(q\) ni toping.

\(2x + 2y\) ko‘phadni ko‘paytuvchilarga ajrating.

\(64 \cdot {9^x} - 84 \cdot {12^x} + 27 \cdot {16^x} = 0\) tenglamaning haqiqiy ildizlari ko‘paytmasini toping.

Quyidagi rasmda tasvirlangan doiralardan eng kattasining radiusi \(4\;{\rm{sm}}\) ga teng.

Qolgan har bir doiraning radiusi o‘zidan oldingi doira radiusining \(\frac{3}{4}\) qismini tashkil qiladi. Bunga ko‘ra barcha doiralarning yuzlari yig‘indisini \(\left( {{\rm{s}}{{\rm{m}}^2}} \right)\) toping.

Quyidagi chizmada olcha daraxtining shoxlari ko‘rsatilgan:

Agar \(AB//ED\) bo‘lsa, \(\angle BCD\) ni toping.

\(\frac{1}{x} + \frac{1}{y} = \frac{3}{2}\) va \({2^x} = {3^y}\) bo‘lsa, \({8^x}\) ning qiymatini toping.

Quyidagi rasmda markazi koordinatalar boshida bo‘lgan aylana tasvirlangan:

\(K\) va \(L\) nuqtalarning absissalari mos ravishda \(\frac{1}{{\sqrt 5 }}\) va \(\frac{3}{{\sqrt {10} }}\) ga teng bo‘lsa, \(\alpha \) ni toping.

\(\sqrt {6x - 57} = 9\) tenglama nechta haqiqiy ildizga ega?

\(3{a^2} - 4ab + {b^2} = 0\) bo‘lsa, \(a\) ni \(b\) orqali ifodalang.

\(x + \sqrt x = 3\) bo’lsa, \(\frac{{3 + x\sqrt x }}{{\sqrt x }}\) ning qiymatini toping.

Slindrning asosi tenglamasi \({x^2} + {\left( {y - 2} \right)^2} = 25\) bo‘lgan aylanadan iborat. Agar silindrning balandligi \(6\;{\rm{sm}}\) ga teng bo‘lsa, uning hajmi necha \(\pi \;{\rm{sm}}\) ga teng bo‘ladi?

\(\left( {\begin{array}{*{20}{c}}{EKUB\left( {x;y} \right) = 45}\\{\frac{x}{y} = \frac{{11}}{7}\;\;\;\;}\end{array}} \right.\) tenglamalar sistemasini yeching.