Kontrol'naya rabota "Proizvodnyye i ikh prilozheniya" (2 chasa). 260 str. 1. Nayti proizvodnuyu pervogo poryadka y′ 2. Nayti proizvodnuyu pervogo poryadka y′ 2.4 y = (1 + ctg23x)e−x 3. Vychislit' pervuyu proizvodnuyu funktsii pri ukazannom znachenii argumenta ili parametra libo pri zadannykh koordinatakh tochki. 3.4 f(t) = ln(1 + a−2t), t = 0 4. Nayti vtoruyu proizvodnuyu y′′ 5. Nayti vtoruyu proizvodnuyu d2y/dx2 funktsii. 6. Reshit' sleduyushchiye zadachi. 6.4. Pod kakim uglom peresekayutsya giperbola y = 1/x i parabola y = √x? 7. Reshit' sleduyushchiye zadachi. 7.4. Skorost' tela, dvizhushchegosya pryamolineyno, opredelyayetsya formuloy y = 3t + t2. Kakoye uskoreniye budet imet' telo cherez 4 s posle nachala dvizheniya?
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Test "Derivatives and their applications" (2 hours). 255 pages

1. Find the first derivative of y′

2. Find the first derivative of y′
2.4 y = (1 + cot23x)e−x

3. Calculate the first derivative of the function for the specified value of the argument or parameter or for the given coordinates of the point.
3.4 f(t) = ln(1 + a−2t), t = 0

4. Find the second derivative of y′′

5. Find the second derivative d2y/dx2 of the function.

6. Solve the following problems.
6.4. At what angle do the hyperbola y = 1/x and the parabola y = √x intersect?

7. Solve the following problems.
7.4. The speed of a body moving in a straight line is determined by the formula υ = 3t + t2. What acceleration will the body have 4 s after the start of the motion?

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