Sketch the product of these, viz., g(t)=u(t-3) u(-t-4) f g(t)dt = u(t-3) u(-t-4)dt Evaluate t=-oo t=-oo Evaluate ) f u(C)dt and (i) f u()dt t-500 t=-oo Sketch the product of these, viz., g(t)=u(t-3) u(-t-4) f g(t)dt = u(t-3) u(-t-4)dt Evaluate t=-oo t=-oo Evaluate ) f u(C)dt and (i) f u()dt t-500 t=-oo
Consider the figure below. y=f(x) Evaluate. 1 ['rs. O 2. /Ral dx = 0 Let A(x) = f(t) dt for f(x) as shown in blue in the figure below. y = f(x) + X 2 3 4 5 6 7 1 Calculate the following. A(2) = A(4) = A(2) = A (4) =
Let F(x) = Sý sin*(0) dt. Evaluate the following limit . Let F(x) = $* sin?(t) dt. Evaluate the following limit. 2022
cos((+dt. (5 pts.) 1 3. Evaluate the integral 8(t)dt. (5 pts.) 4. Evaluate the sum Σ 23]n]. (4 pts.) 2 +2 +2 + 2+2 4 2
3. Evaluate: The value f(4) for the continuous function f satisfying 2 sin = f(t) dt
Let A(x)=∫(bounds 0 to x) f(t)dt, with f(x) as in figure. Let A(z) = J f(t) dt, with f(z) as in figure. -1 -2 A()l has a local minimum on (O A(z) has a local maximum on (0, 6) at a 6.5 Let A(z) = J f(t) dt, with f(z) as in figure. -1 -2 A()l has a local minimum on (O A(z) has a local maximum on (0, 6) at a 6.5
dn (a) Show that L[i" f(t)] = (-1)" (t) for any positive integer n 2 1 dsn a d K(s, t)f(t) dt / ) est = tne-8t and assume that K(s, t)f(t) dt. Hint: (-1)" as ds (b) Use the above formula to compute L[t? cost]. dn (a) Show that L[i" f(t)] = (-1)" (t) for any positive integer n 2 1 dsn a d K(s, t)f(t) dt / ) est = tne-8t and assume that K(s, t)f(t) dt. Hint:...
3) Let F(x) = {* In In(1+t) dt. t (a) Find the Maclaurin series for F: (b) Use the series in part (a) to evaluate F(-1) exactly and use the result to state its interval of convergence. (c) Approximate F(1) to three decimals. (Hint: Look for an alternating series. )
Problem 2. Evaluate the following integrals: a) (t+1)8(t-1)dt b) ſ exp(-+)$(t + 2)dt c) Itsin() 062 – 1)dt
(1 point) Let F(x) = ļ," f(t) dt, where f(t) is the graph in the figure. Find each of the following: 2 A. F(2) = 0 B. F'(4) = 2 5 69 7 C. The interval (with endpoints given to the nearest 0.25) where F is concave up: interval = (1.5, 4.5) (Give your answer as an interval or a list of intervals, e.g., (-infinity, 8] or (1,5),(7,10), or enter none for no intervals.) D. The value of x where...