please comment if you have any doubts will clarify
5. Let F(x) = Lt tet-2+tº +1 Edt, find F'(2) tt +3
نه 2 5. Let F(x) = - [ « tet-2 + t3 +1 dt, find F'(2). tt + 3
5) Let F(t) te), te,t >for t e R. Find (t)dt. 0 te, tet, tdt 0
g3ه 5. Let F(x) = وب tet-2 + t3 +1 - dt, find F (2). tt + 3
Problem 9. (5 points) If z= sin (5), x = 3t, = 5 – tº, find dz/dt using the chain rule. Assume the variables are restricted to domains on which the functions are defined. dz dt = preview answers Problem 10. (5 points) Find the partial derivatives of the function f(x, y) = cos(-3t² + 4t – 8) dt y f1(x, y) = fy(x, y) =
3) Let F(x) = {* In In(1+t) dt. t (a) Find the Maclaurin series for F: (b) Use the series in part (a) to evaluate F(-1) exactly and use the result to state its interval of convergence. (c) Approximate F(1) to three decimals. (Hint: Look for an alternating series. )
(1 point) Let f(x) = [: to dt. Evaluate the following. f'(x) = f'(5) =
Let F(x) = ſ vt(t+1) dt. Find F'(x) (again, the derivative!!). In()
1. Let f(t) e-2/3. Show that f(t)dt = 1 and that if X is a random variable with density f, then for all a 〈 b
The graph of f is given to the right. Let g(x) = | FO) dt. 2 v=f(x) 1 3 -2 1 0 1 2 1 X -2 (a) Find g(1). (b) Find g'(-2). (c) Find g'(1). (d) On what interval is g increasing?