MATH 139 Midterm: MATH139 Fall 2003 Exam

ool Careruly. maRe sure you are answering the que correctly I) y =x" + 2x Find where the slope of a tangent line is equal to 3 2) Differentiate each of the following functions a) y =-6x-4 2) Determine if the function has any horizontal tangent lines b) g(x)-re2x c) y=x2/3-74/3 3 24X 2 r +1 2 y = 2-x3 3) Use the quotient rule to show that the derivative of y = sec θ is y' = sec θ tan θ 4) Find the derivative only three of the following functions. Simplify each answer as mu possible a) f(x)=x' cos x b) f(x)= b) f(x)= 4x-21 y=ln(x5) c) -7 4t +5 e)y3x21 f) g(x)=cos(x3+4)

Use techniques of differentiation to find the derivative of each of the each of the following functions and simplify your answers. f (x) = x 4 ln x g(x) = x2 + 3x/x2 - 1 h(x) = ln(ex2 - x + 2x - 1) p(t) = (t + 1)5 (t3 + 2t2 + t - 1)2/3 (6 - t)2

1. Find the following limits: (Use L'Hopital's Rule if applicable.) es points each) 6x2 +3x-7 9x2-5x +6 b. lim1-3x c. lim 2-3x+I c. lim 2x-10 2x +10 2x-10 f. lim+25 e. lim dyê·¸ dx ax ( 5-5) 50 h. lim+4-3 i. lim g. lim lim C-53) dy ex-1 ax unce Fined X-5)(x +4 xfut3