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f(y)=sinx+cscx²y+2xy

f(x)=cotx+tanx²-2cosx²


f(y)=cotx+tanx²-2cosx²
f(y)=cotxy+coty²+yx²
For the function f, defined by f(x)=4x^3-4x^2-7x-2 there
exist a point C ∈ ]-1/2,2[ satisfying f′(c)=0.
F(x)=sinx²
d/dx int 1 to rootx tan^2(t^2)dt
Prove that root of 2 plus root of 3 is irrational

Volume flow rate of water flowing in the pipe Q = 𝑑𝑉/𝑑𝑡 [m^3/ h] varies with time as follows: Q (t) = 5 + 2cos^2 (πt/12). How many cubic meters of water is flowing through the pipe through the day? (the unit of time is an hour)


In a water bath with an area of ​​A = 10.0 m^2 and depth h = 1.5 m, temperature is initially T0 = 4 ° C throughout. The water is heated so that finally the water the temperature follows the equation T (z) = T0 + 15e^+0,5z in the depth direction[in ° C]. The temperature coefficient of water volume is y = 500 x 10^-6 1/°C. How much has the pool water volume increased during heating?
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