=3. (2 points) Let f(x) dx (a) What is the average value of f(x) on the...
4. Let f(x) = (in x)? (a) Find the average value of f on the interval (1, e]. (Hint: use integration by parts.) (b) Find the value c such that f(c) equals the average value found in part (a).
answer all with clear handwriting please.
2. (4 points) Let f(x) = x - 9x - 36x”. Find the zeros of the function algehraically (by factoring). and give the exact multiplicity for each zero (not just odd/even). State the behavior of the graph at each zero (whether the graph crosses the x-axts or touches the x-axts and turns around at each zero). Zero Multiplicity Behavior 3. (4 points) Solve the following inequality and graph the solution set on a Real...
(1 point) Let [ f(z)dx=-13, 5° f(x) dx = 3, $*g(x) dx = 6, §*9(a) dx = 1, J2 Use these values to evaluate the given definite integrals. a) ["{$(2) + 9()) dx = 6 .) – g(x)) dx = * (31(2) + 29(2) de = (af(x) + g()) dc = 0. d) Find the value a such that a=
Suppose f(x) is an even function on the symmetric interval x 6 [-A, A] and g(x) is an odd function defined on the same interval. Which of the following must be true? A/3 A/3 84(3x) + 1 dx = 2 84(3x) + 1 dx -A/3 0 f(x) is not an odd function. A/2 A/2 ✓ f(x) dx = 2 ✓ f(x) dx -A/2 A | f(x)g?(x) dx = 0 -A
help me with these two probability questions.
12. (3 points) Let f(x) = kx3 +2 -1 for 0 <3 <1, and f(2)= 0 for [0, 1], where k is some unknown constant. What value of k will make f a valid probability density function? A. 1/4 B. 1/3 C. 1 D. 2 -xel + Ž - 1=1 | LEH , E = Ž- at zlik Ks6 나 E. 4 F. 6 G. No such value of k exists + C....
(b) (3 points) Let p(x) = x + x Show that this function is neither odd nor even Then, show that the function defined by h(x) = P(x) - P(-x)] is an odd function 4. (6 points) (a) (2.5 points) Let f(x) = Vä? - 1 and g(x) = (f)(x) and its domain. . Find the product function
1. If fand g are both even functions, is the product fg even? If f and g both odd functions, is fg odd? What if f is even and g is odd? Justify your answers. (10 points) Find the domain g(x) =-. (10 points) 2. of the composited function fog, where f(x)=x+ and x +1 x+2 3. Let ifx <1 g(x) = x-3 ifx >2 Evaluate each of the following, if it exists. (10 points) lim g(x) lim gx)(i) lim...
What is the average value of the function f(x) = lnm on [1,4]? O A. 0.3034 OB. 0.3203 OC. 0.3402 OD. 0.3624 O E. 0.3802 If $3° f (x)dx = }, what is Sz" (f (x) + 4.)dx? o A. 73 0 0 0 OD. O E. - 31 If Sö eºdx = e2 – 1, what is Sze7-3dx? O A. e2 - 1 OB. e3 - 1 OC. e5 - 1 o D. et O E. 1] (e2 -...
3. (25 points) Let f(x) = 2/2_8 (a) Find the domain of f. (b) Find the equation of all vertical asymptotes or explain why none exist. For each vertical asymptote = a, calculate both the one-sided limits limo+a+ f(x) and limo-ha-f(T). (c) Find the equation of all horizontal asymptotes or explain why none exist. C Bollett. ollett (d) Let g(x) = f(x) if x 70 For what value of b would g(x) be continuous at I=0? (or if no 91...
(3 points) Let $*fdx = 5, $*f6wdx=-11, 6 s6wdx= 11, $* sco) dx = 4, Use these values to evaluate the given definite integrals. 2 a) / (f(x) + g(x)) dx = b) fºr(x) = g(x) dx = on f* 3F() +29(e) dx = d) Find the value a such that / (af(x) + g(x)) dx = 0. a =