Test 2
2001, Fall

Version A

Elementary functions. 2+3+3+3+4 = 15 points.

Sketch the graph and give the domain of the following functions!

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

Algebraic rules. 10 points.

Find the following values!

((sinπ)/6), 	((tanπ)/3),	(27^(1/3)),	 	(Subscript[log, 2]) (1/8), 	(10^lg2).

Derivatives. 3+4+7+8+8 = 30 points.

Differentiate the following functions!

(x^2)+cos 2 x-π, 	(Sqrt[x+2])lnx +(Sqrt[2]), 	(x^3 - x^2)ln((x^2)+1),		(((e^x) tan x)/((x^2)-2 x-1)), 	(e^(^(x+(Subscript[log, 2]) x))).

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. 30 points.

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

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