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.

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

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

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

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

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

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

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

\(x \ne 10\) 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.

\(ABCD\) 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.

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

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

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

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.

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.

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

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

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

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

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

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

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

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

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

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

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

Quyidagi chizmada olcha daraxtining shoxlari ko‘rsatilgan:

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