g3ه 5. Let F(x) = وب tet-2 + t3 +1 - dt, find F (2). tt + 3
نه 2 5. Let F(x) = - [ « tet-2 + t3 +1 dt, find F'(2). tt + 3
5. Let F(x) = Lates te-2 +tº+1 -dt, find F'(2) 1 + 3
a box with a square base
.6 4. Compute x + 3x4 + 2x3 + 1 -da. 24 일 5. Let F(x) = tet-2+tº +1 dt, find F'(2). tt +3 0 -. A box with a square base and open top must have a volume of 500 cm. Find the dimensions of the box which minimize the amount of material to be used. 2. Draw the graph of f(x) = x ln(1x) - (x - 4) In(x - 41).
tet 3. Let (1 3 3 A= 0 1 3 . f(t) = 0-3 1/ Find the general solution to i' = AT + f. -3te2t \(t+11)e24
8. Let f(x)- -132+1, n-1 (a) (10) Find the radius of convergence R of f. (b) (ao) Use the given power series to find an approximation of f(edt that has an error of less than 0.001. Don't simplify your answer.pproximationofhuamathathasanemor
8. Let f(x)- -132+1, n-1 (a) (10) Find the radius of convergence R of f. (b) (ao) Use the given power series to find an approximation of f(edt that has an error of less than 0.001. Don't simplify your answer.pproximationofhuamathathasanemor
Problems 5) Let (X, M, u) be a measure space, and f e Lt. Assume that S fdu = 1. Prove that 00, 0<a<1, lim n ln (1 +(${2))a) du(x) = { 1, a = 1, 10. a 1. Hint: Use Fatou's lemma for a < 1 and LDCT for a > 1 (dominate by af). 1+00)
5 (10 pts) Let b 0 be a number and f)for (o.b, Lt artition of [O, b, wherefor0, 1,2, ns bea 72 ( 1) Find the upper sum U(f, P) . (2) Find lim Uf. P).
5 (10 pts) Let b 0 be a number and f)for (o.b, Lt artition of [O, b, wherefor0, 1,2, ns bea 72 ( 1) Find the upper sum U(f, P) . (2) Find lim Uf. P).
x²+2x+2 4. Let y=f(x)= x² – 3x-5 (a) Find f(3) (b) Find and simplify f(x) - $(3) X-3 f(x)- $(3) (c) Find lim X-3 (d) Find and simplify $(3+h)-f(3) h 13 (e) Find lim f(3+h) – S (3) h 0 h (t) Find the slope-intercept form of the tangent line to y = f(x) at x = 3. (g) Plot the curve and the tangent line on the same graph, using the form on the window (-3,7]*[-10,10). 5. A car...
5) Let F(t) te), te,t >for t e R. Find (t)dt. 0 te, tet, tdt 0