Math 7
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2.2 Find the derivative of the function using the definition of derivative. State the domain of the function and the domain
of its derivative.
(1) f(x)=(1-x)/(2+x)
(2) f(x)=\sqrt(7-2x)
2.4 Find the limit.
(1) \lim_(x->1)(sin(x-1))/(x^(2)+x-2)
(2) \lim_(x->0)(sin4x)/(sin6x)
(3) \lim_(x->(\pi )/(4))(sinx-cosx)/(cos2x)
2.5 Suppose that w=u@v and u(0)=1,v(0)=2,u^(')(0)=3,u^(')(2)=4,v^(')(0)=5, and v^(')(2)=6. Find w^(')(0).
2.5 Differentiate
(1) y=\sqrt(secx^(3))
(2) f(x)=sin(cos(tanx))
(3) ,g(t)=((t-2)/(2t+1))^(9)
2.6 Two curves are orthogonal if their tangent lines are perpendicular at each point of intersection. Show that given curves
are orthogonal. Refer to 2.6 Homework #51, 52, 53.
(1) x^(2)+y^(2)=r^(2),ax+by=0
(2) x^(2)+y^(2)=ax,x^(2)+y^(2)=by
(3) y=cx^(2),x^(2)+2y^(2)=k
(4) x^(2)+(y-c)^(2)=
