Find the derivative of the following. ga) - J. (+ vt - t) dt g'(x) = (22=2+x= x2) *
8. Find the derivative of F(x) = 322(t + 2) dt
Jo (2-x) dx 12. (3pts) Let f(t) be a continuous function. Find the derivative of y = f(x).Sh(t) dt. 12
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. )
please do all 3 1. (3 points) Find the derivative of F(x) = (t +2) dt. (You may assume that æ is restricted to an appropriate interval (a, b), so don't bother with any issues about that.) 42.2 - - 6 d. 2. (4 points) Evaluate 2 - 3 3. (3 points) Solve the equation sint dt = 0 for x where < <
8. [0/5 Points] DETAILS PREVIOUS ANSWERS Find the derivative of the function. f(t) = 43/2 log&(vt + 3) 1 3x?loge (Vx+3) 3 2 f'(t) = X + 2 2 ln(6)(x+3) x
(1 point) A. Let g(t) be the solution of the initial value problem dy dt with g(1)1 Find g(t) B. Let f(t) be the solution of the initial value problem dy dt with f(0) 0 Find f(t). C. Find a constant c so that solves the differential equation in part B and k(1) 13. cE (1 point) A. Let g(t) be the solution of the initial value problem dy dt with g(1)1 Find g(t) B. Let f(t) be the solution...
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
Let A(x)=∫(bounds 0 to x) f(t)dt, with f(x) as in figure. Let A(z) = J f(t) dt, with f(z) as in figure. -1 -2 A()l has a local minimum on (O A(z) has a local maximum on (0, 6) at a 6.5 Let A(z) = J f(t) dt, with f(z) as in figure. -1 -2 A()l has a local minimum on (O A(z) has a local maximum on (0, 6) at a 6.5
(1 point) Compute the derivative of F(x) if F(x) = 5 * 31 dt F'(x) = 0 08