Given X ~ N(1,22 ):
a. P(X2− 2X < 3) =?
b. E(X2 − 2X) =?
QUESTION 5 2x Given that f(x)= is continuous and decreasing on [3,+). x2 +4 Determine the convergence of x2 2x i) dx. 3 +00 2n ii) State the convergence of the series - Justify your answer. n=3 n° +4
2x f(x) = ex+ f'(x) = (3x + 2) ex+3 B f'(x) = (x2 + 2x) e*+2x-1 С f'(x) = ex®+2x f'(x) = €3x+2
Given output, y[n] = 2x[n] + x[n 1] + 3 Determine wether the systema) Memory b) Causal c) Linear d) Time Invariant e) Stable
using the general power rule Question 1 let y = (x2 +x)3 Find y' 2x+1 3(x2+x)2 3(x2+x)2 (2x+1) • (x2+x)2 (2x+1) recall general power rule formula has three parts: [u(x)" ]' = n u(x)" 1 u'(x) Question 2 let y = (x3 +x2) 1/3 Find y' (x3 +x2) 1/3 (1/3) (x3 +x2) 1/3 . (1/3)(x3 +x2)-2/3 (1/3)(x3 +x2-2/3 (3x2+2x) recall general power rule has three parts. [u(x)"l' = n u(x)n-1 u'(x) Question 5 let g(x) = 1/(x3+x2)3 find g'(x) (x²+x23...
QUESTION 4 Given f(x)=2x-5 and g(x)= x2 + x - 20, find each: a) [fog)(3) b)[gºf](x) IT I Arial 3(12pt » T.:= . 31.25
P(x) = x2-2x-15, find the instantaneous rate of change at x = 2. 7, For the function a. -15 b. 3 c. d. 0 None of the above e. If the total revenue function for a blender is 8. R(x) = 36x-0.0 1x2 where x is the number of blenders sold, what is the average rate of change in total revenue Rix) as x increases from 10 to 20 blenders? a. $34.00 b. $356 c. $35.70 d. $35.50 None of...
Given f(x) and g(x), find the following. 3) f(x) = x2 + 2x and g(x)= x + 9. (fg)(x)
2. Sketch the graph of the following functions and find the values of x for which lim f(x) does not exist. b)/(x) = 1, x = 0 f(x)- 5, x=3 c) x2 x>1 2x, x> 3 d) f(x)-v e) (x)- [2x 1- sin x Discuss the continuity of the functions given in problem #2 above. Also, determine (using the limit concept) if the discontinuities of these functions are removable or nonremovable 3. Find the value of the constant k (using...
8. [16 pts total] Given x E Z and P(x): "x2 + x is even", answer the following questions. (a) [3 / 16 pts] If x is even, prove 3x P(x). (b) [3 / 16 pts) If x is odd, prove 3x P(x). (c) [10 / 16 pts] Prove Vx P(x).
5x3-12x2-1 x2-2x 5. Find the equations of the asymptotes of f (x) Show that P(-3, 2, 0) is the minimum point of the function 6. z=x2 +3y2 +2xy + 2x-6y +9.