Please write clear and put the answer between square If 31 - 3 < f(x) <...
X+2 X<3 n. lim f(x), where f(x)= { x3 12-2x x>3 3
Question 9 Find 5x+1 f(x) dx given that f(x) = { 3-x 0<x< 1 1<x<3 =la ole ala ala T
F'(x) < 0 if 0<x< 2or x > 4 f"(x)>0if1<x<3, F"(x)<0if x<lor x>3 4. Find the limit. lim(1-2x) 10 5. What is the minimum vertical distance between the parabolas y = x + 1 and y=x-r 4.pdf
If 4 - x2 = f(x) < 4+x2 for –3 <x<3, find lim (2) 20
Suppose f'(x) = -1/3(x+3). On what open interval(s) is f(x) decreasing 0-3 < < 0 0-3 <x<0 0 - < I< -3 0 - < ?<-3 and 0 < x < 0
2. A random variable X has a cdf given by F(x) = 1 . x < 0 0 < x < 1 <3 x > 3 11, (f) What is P(X = 1)? (g) Find E(X), the expectation of X. (h) Find the 75th percentile of the distribution. Namely, find the value of 70.75 SO that P(X < 70.75) = F(710.75) = 0.75. (i) Find the conditional probability P(X > X|X > 3).
(2.2) Let a be a real number with 1<a< 2. Put f(x) = Q +r 1+2 (a) Show that f maps (1, 0) into (1, 0). (b) Show that f is a contraction on [1, ) and find its fixed point.
(Hint: think of tan as a fraction!) lim (1 - .) tan 7. Suppose a function f(x) satisfies f'(x) < 0 and f(x) > 0 for all x 20. > 0 for all x > 0. Consider the function F(x) := ["s(t) dt whose domain is 0,00). Is F(x) an increasing or decreasing function
Find the extreme values of 'f' on the region described by the
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22. f (x, y) = 2x2 + 3y2 – 40 – 5, x2 + y2 < 16
7. The vector field F =< 3x2z In y + ze+2 +20, - 3y?, x° In y + ce2 +423 > is conservative. Find a potential function f(x, y, z) such that F=Vf. Y