20 marks) 1. Estimate the instantaneous rate of change of f(x) - x at x =...
Calculate the work done by the vector field F(x,y)=4xy, 2x2 along a smooth, simple curve from point (3, −1) to point (4, 2) We were unable to transcribe this imageWe were unable to transcribe this image
(a) For what value of x does f(x) = g(x)? (b) For which values of x is f(x) >g(x)? For every x in the interval f(x)>g(x). (Type your answer in interval notation.) In parts (a) and (b), use the given figure. (a) Solve the equation: f(x) = g(x). (b) Solve the inequality f(x) > g(x). у y = g(x) y = f(xN (-9,7)
* For the function f(x) = (3x + 5 if x 20 6 if x < 0. find f(-10)
f(x,y)= 0 1. (15 marks) Suppose X and Y are jointly continuous random variables with probability density function 12, 0<x<1, 0<y<0.5 else a) (5 marks) Find P(X - Y <0.25). b) (5 marks) Find P(XY <0.30). c) (5 marks) Find V (2x - 5Y+30).
Solve the inequality f(x) <0, where f(x) = - x2(x + 4), by using the graph of the The solution set for f(x) <0 is. (Type your answer in interval notation.) function. Ay 4- 2- х 500 -8 -6 -4 -2 2 4. 6 -8- -104 -12-
Given that 0<x< 2π, solve the followi ing inequalities. (2) 2sin2x <3cosx (3) 2cosx3 sinx+10
(9) Stokes' Theorem for Work in Space F(x, y, z) =< P,Q,R >=<-y+z, x - 2,x - y > S:z = 4 - x2 - y2 and z>0 (9a) Evaluate W= $ Pdx + Qdy + Rdz с (9) Stokes' Theorem for Work in Space F(x, y, z) =< P,Q,R>=<-y+z, x - 2, x - y > S:z = 4 - x2 - y2 and z 20 (9b) Verify Stokes' Theorem.
Question 9 Evaluate the integral f(x) dx where 203 f(x) = for x <1 for x > 1 6 7 4 5 3 O2 11 2
f(x,y)=0 2. (20 marks) Suppose X and Y are jointly continuous random variables with probability density function fc, 0<x<1, 0<y<1, x + y>1 else a) (2.5 marks) Find the constant, c, so that this is valid joint density function. b) (5 marks) Find P(Y > 2X). c) (5 marks) Find P(X>0.5 Y = 0.75). d) (5 marks) Find P(X>0.5 Y <0.75). e) (2.5 marks) Are X and Y independent? Justify your answer citing an appropriate theorem.
Let f(x)= if , if if a) What is the fomain of f(x)? Write in interval notation. b) Determine the y-intercept of the function, if any. Make sure to justify your answer. c) Determine the x-intercepts of the function, if any. Justify your answer. We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this...