Problem 3: Show that cosh ax dx = 1 cosh x^4 *2cos (ra/where (al<1 om dx...
(1 point) i * f(x) dx = 3 and ' s(x) dx = 4, what is the value of [ f(xBC) da where D is the rectangle: 3 < x < 4, 3 sy s 7?
Evaluate the integral. 3 4 [ rwa f(x) dx where f(x) = 15 - x2 if -3 SXO if 0<x<3
for all points on the graph of y = 2cos x+5 where the slope of the 6. Find the values of x in OSx< tangent line is -1. (10 pt) be
Integrate the function. - dx, x<2 De 10, x2 om (2nd OB. a 1703 12 +0 oc. (4-2) ?. Oo. (1-2) 112* 12y3 3 / 2 + ) 1/2
3:13 Calculator Close dx = 22 X VX +4 We don't know how to calculate the entered A math problem... + fj<> abc + + ( ) 7 8 9 3. VO. 4 5 6 0²8.123 . % 0 . =
Let X N(1,3) and Y~ N(2,4), where X and Y are independent 1. P(X <4)-? P(Y < 1) =? 4、 5, P(Y < 6) =? 7, P(X + Y < 4) =?
(4) Let f(x) (0 if x<0 (a) Show that f is differentiable at z (b) Is f'continuous on R? Is f continuous on R? Justify your answer.
T (1 point) Evaluate f(x) dx, where J12) f(x) = { 2.2 -ASX < 0 | 3 sin(x), 0 < x < 1. [fle) de =
Find all the generators of each of the following cyclic groups a. The even numbers under addition b. c. d. {Z20, +} <a> where a = 15 <a> where al = 15
2. For the difference cquation, X2+] = ax, + b = f(x,), where 0 <a < 1 and b> 0, use the solution given in (1.12) to find the following limit: lim ->XX7. Show that this limit is also a fixed point of the difference cquation, that is, it is a solution x of t = f(x) (see Figure 1.2).