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.

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

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

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

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

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

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

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

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

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

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.

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

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

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

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

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

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

Quyidagi chizmada olcha daraxtining shoxlari ko‘rsatilgan:

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

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

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

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?

\(x \ne 10\) 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.

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.

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

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