Test 2
2002, Fall

Mixture. 5 points.

How much of 30% and 50% concentrated solutions should be mixed to obtain 10 kg solution of 34% concentration?

Elementary functions. 10 points.

Write the domain and plot the graph of the following functions!

(2^(-x))+1, 	(1/(x-2))+1, 	1- (Subscript[log, 3])x, 	sin2x, 		(Sqrt[x-3]).

Functions. 10 points.

Determine the domin of definition for the function f(x) = (Sqrt[-2+x+(x^2)])+(1/(x-1)).

Inverse function. 10 points.

Find and plot the inverse function of f(x) = 1-lnx

Derivative. 6+7+7 points.

Differentiate the following functions!

(x^3) (Subscript[log, 2])x, 	((3^x)/((x^2)-2 x-1)), 	(e^(-(x^2))).

Tangent line. 10 points.

Find the equation of the tangent line of f(x) = sin((x^2)) at (Subscript[x, 0])=(Sqrt[(π/3)])!

Secant line. 5 points.

Find the equation of the secant line of f(x) = (Sqrt[-x+(x^2)]) at (Subscript[x, 0])=1, (Subscript[x, 1])=2!

Investigation of a function. 25 points.

Do the total examination (domain, zeros, monotonicity, extremal points, concavity, inflection points, limits at plus and minus infinity, graph) of the following function!

f(x) = 18(x^2)- (x^4)

Elementary antiderivatives. 10 points.

Find the following antiderivatives!

∫x((x^2)-(Sqrt[x])) dx, 	∫sin2x - (x^(1/3))dx.