1. (30%) True and False. (1) D(f(x)*g(x))=Df(x)*Dg(x). (2) DJf(x) =Df (x) (3) f ( x) =Vx is continuous and differentiable everywhere for all x 20 (4) D[f(x)"]= n*f(x)"- D(f(x)) is true only if n is an integer. (5) / (x) => is continuous for all x but not differentiable at x=0. (6) X - C lim of(x) may or may not equal to f(c). (7) A function f is continuous at x = a if and only if lim f(x) = f(a). (8) If y=f(x) is differentiable at x=a then f is continuous at x=a. (9) The function ) =X - 10x +5 has a horizontal tangent line at x=5. (10) If f is not continuous at x=a then f(x) is not differentiable at x=a. (11) If f'(x)=constant for all x, then f must be a linear function of x. (12) If f'(a)=0, then the tangent of the function f at x=a is a horizontal line. (13) D(f(x)-g(x))=Df(x)-Dg(x). (14) if F(x)=f(x)*g(x) is differentiable at x, then DF(x)=f(x)Dg(x) +g(x)Df(x), implying both f and g are differentiable at x. (15) D(e*)=x*e*-1