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2) Find the area bounded by the curve x = y² + 2y and the line x = 3.
1) Find the area bounded by the curve y-9-x and the x axis.
a) Horizontal Strip
b) Vertical Strip
The following values show the IQ and the Entrance Exam scores of incoming freshmen in a certain university.
Student
IQ (x)
Entrance Exam scores (y)
1
120
98
2
85
78
3
90
88
4
110
95
5
115
97
6
124
99
7
89
88
8
98
92
9
99
93
10
100
91
Calculate the following:
a. Compute the value of correlation coefficient ®.
b. What is the least-squares equation?
c. If student 11 has an IQ = 130, what is his/her estimated entrance exam score?
The following table gives the recorded grades for 10 students on a midterm test and the final examination in a statistics course.
Student
Midterm Test
Final Examination
1
84
73
2
98
63
3
91
87
4
72
66
5
86
78
6
93
78
7
80
91
8
9
92
88
10
87
77
a. Calculate the rank correlation coefficient.
b. Test the hypothesis @ .05 level of significance.
The probability density function of two random variables is f(x1,x2)=e-(x1+x2) x1>0 , x2>0 given that y=x1/(x1+x2)what is the probability density function of variabley
Consider the R^2 - R function f defined by f(x,y) = (x^2 +y)/y.
Determine each of the following limits,if it exists.
a) lim (x,y) -> (0,0) f(x,y),where C1 is the curve y=x
b) lim (x,y) -> (0,0) f(x,y),Where C2 is the curve y=2x
c) lim (x,y) -> (0,0) f(x,y),Where C3 is the curve y=x^2
d) lim (x,y) -> (0,0) f(x,y)
Let f be the R^2 - R function defined by f(x,y) = ln xy and let r be the R-R^2 function defined by r(t) = (e^t,t).
a) Determine the composite function f o r?
b) Determine grad f(x,y) and r' (t)?
c) Determine the derivative function (f o r)' by
i) Differentiating the expression obtained in (a)?
ii) Using the Chain rule?
Consider the R^2 - R function defined by f(x,y) = 3x + 2y.
Prove from first principles that lim (x,y) -> (1,-1) f(x,y) = 1
let f be the R^2-R function defined by f(x,y) = (x - y)^3
a) Determine the rate of increase in f at the point (2,1) in the direction of the vector (1,-1)?
b) What is the rate of increase in f at (2,1) in the direction of the negative X-axis?
c)Determine the maximum rate of increase in f at (2,1).In which direction is the maximum rate of increase?
Use resolution to show the hypotheses “Allen is a bad
boy or Hillary is a good girl” and “Allen is a good boy or
David is happy” imply the conclusion “Hillary is a good
girl or David is happy.”
