• San Jose State University

• MATH 30

SJSU MАТH 30, Midterm 2, Instructor: Plamen Koev Write all answers on this sheet of paper. Only this sheet will be graded. 1. (10 points) Let f(x) = e*+ (a) f is defined for the following values of x: (b) f'(x) = ex (x-i) x2 (c) f"(x) = ex(x2-2x +2) 3 All real numbers except for x=0 - (d) f'(x) = 0 at the point(s): =1 (e) f"(x) = 0 at the point(s): DOES NOT EXIST (f) f(r) is decreasing on the interval (s): ( il (g) f(x) is increasing on the interval(s): (1,00) (h) f(x) is concave up on the interval(s): (C, 0D) (i) the local minima are at (if they do not exist, indicate so): x=l is e+l (j) the inflection points are (if they do not exist, indicate so): Dos NOT EXIST. 2. (5 points) Compute the limit tan x +2 sin x 10 lim 20 -3 2x 2 5 Sec²(x) + 2cos x 2 cos (a) +2 3 lim こ Cos2(o) 2 lim 2 2 70 3. (5 points) Compute the limit lim (secx) 2-0 1/2 e 5 2 lim In (secx) 4т0 e Inlsecx) lim X2 e ¥-90 (Secx tonx) lim メ In(secx) x2 lim tanx Secx lim exo 2x e 2x e Soc(a Sec2(x) 2 e2 SJSU Math 30, Final exam, F 14, Plamen Koev Name: Closed book. Closed notes. No calculators. Show your work. 1. Compute the derivative of 12. ex sin 3x 2. Compute the derivative of xln(x) sin² x 3. Find the equation of the tangent line to the curve defined by y cos = x² + y² at the point (0, 1). 4. Find the absolute minimum and absolute maximum of 3x4 +4x³ – 12x2 + 1 on {-2, 0]. 5. Compute the limit 6. Compute the limit x+ sinx lim x0 x — cosx lim (cosz) 20+ 7. Compute the limit 81x lim x1/x 8. Find f(x) if f"(x) = 6x - sin x, f'(0) =1, and f(0) = 0. 9. Find the interval(s) on which f(x) =3x5 - 20x³ is increasing and concave down (at the same time). 10. Determine if f(x) = 1