a b' lim

Q: Extreme values Find the local extrema of the function g (x) = x2/3(2 - x).

A: Given g (x) = x2/3(2 - x). We need to find the local extrema.

Q: Find the volumes of the solids generated by revolving the regionsbounded by the lines and curves abo...

A: Given x=5y2 , x=0 ,y=-1 ,y=1

Q: Find simpler expressions for the quantities eln 7.2

A: Given expression: eln7.2 We know that  exln(a)=ax Then, eln7.2=e1ln7.2eln7.2=7.21eln7.2=7.2  

Q: express each vector in the form w = w1 i +w2 j + w3 k. 5u - v if u = [1, 1, -1] and v = [2, 0, 3]

A: Given u = [1, 1, -1] and v = [2, 0, 3] To find w=5u-v

Q: Compute the matrix exponential eAt for system x’= Ax given in the following Problem   x’1 = 5x1 - 4x...

A: To Determine: Compute the matrix exponential eAt for system x’= Ax given in the following Problem  G...

Q: Evaluate the series or state that it diverges.

A: Given: S=∑k=0∞120.2k+320.8k for finding given summation, first we expand given expression so, S=∑k=0...

Q: Find the value or values of c that satisfy the equationƒ(b) - ƒ(a)/b - a = ƒ'(c)in the conclusion of...

A: To find the value or values of c that satisfy the equationfb-fab-a=f'cin the conclusion of the Mean ...

Q: Evaluating limits graphically Sketch a graph of f and use it to make a conjecture about the values o...

A: fx=x+2+2,  a=-2 The graph is,

Q: Verify the following property of the twiddle factor: WN2=WN/2

A: we have to verify the property of the twiddle factor. WN2=WN/2

Q: For the following equation, find three ordered pair solutions by completing the table. Then use the ...

A: We have equation of line y=-3x+4   When x=0 then y=-30+4=4 When x=1 then  y=-31+4=1 When x=2 then y=...

Q: Equations of tangent linesa. Find an equation of the line tangent to the given curve at a.b. Use a g...

A: given, y=x+5x-1; a=3we have to find an equation of the tangent line to the given curve at a.and we h...

Q: Explain the operational determinant?

A: The operational determinant :- Consider a system of two linear differential equation  L1x+L2y=f1t L3...

Q: Give a geometric description of the following sets of points. x2 - 4x + y2 + 6y + z2 + 14 = 0

A: It is given that, x2-4x+y2+6y+z2+14=0We have to give a geometric description of the following sets o...

Q: find the velocity and acceleration vectors in terms ofur and uθ . r = a(1 - cos θ) and dθ/dt = 3

A: Given: r=a1-cosθ, dθdt=3

Q: Verify that the general solution satisfies the differential equation. Then find the particular solut...

A:  Given general solution is 3x2+2y2=C.......(1) Differentiating it with respect to y 6x+4yy'=0⇒23x+2y...

Q: Fill in the blank/s: Consider the equation √(2x + 1) = x - 7, Sqauring the left side and simplifying...

A:

Q: The cost (in dollars) of producing units of a certain commodityis C(x)  =5000 +10x +0.05x2.(a) Find ...

A: Given Cx  =5000 +10x +0.05x2.(i)x=100 to x=105Average rate of change=y2−y1x2−x1Average rate of chang...

Q: Evaluate each geometric sum.

A: The given geometric series in summation form is: ∑k=083k To evaluate this series first expand that, ...

Q: Find the product. [8y + (7 - 3x)][8y - (7 - 3x)]

A: Consider the given expression, 8y+7-3x8y-7-3x apply the algebraic identity a+ba-b=a2-b2 8y+7-3x8y-7-...

Q: give a geometric description of the set of points inspace whose coordinates satisfy the given pairs ...

A: Consider the set of points in space whose coordinates satisfy the given pairs of equations. x2 + y2 ...

Q: Find the exact value of cos-1 (-√3/ 2).

A: Given that, cos-1-32 Consider, θ=cos-1-32 Now take the cosine on both sides. cosθ=coscos-1-32cosθ=-3...

Q: Explain how to sketch a contour map of a function of x and y.

A: When drawing in three dimensions is inconvenient, a contour map is a useful alternative for represen...

Q: A silo (base not included) is to be constructed in the form of a cylinder surmounted by a hemisphere...

A: Let r and h be the radius and heights of a cylinder which is covered by the radius r of a hemisphere...

Q: Find an equation of the normal line to y = x2 at the point (2, 4). (The normal line at a point is pe...

A: y=x2 Differentiating with respect to x, we get dydx=2x Now slope of the tangent line at 2, 4 is, dyd...

Q: Write each equation in its equivalent exponential form: a. 2 = log5 x  b. 3 = logb 64  c. log3 7 = y...

A: We have to write equation in equivalent exponential form: a. 2=log5xb. 3=logb64c. log37=y We know th...

Q: The displacement s (in meters) of a particle moving in a straight line is given by the equation of m...

A: The given displacement is: s=4t3+6t+2 To find the instantaneous velocity of the particle at time t s...

Q: Evaluate exponential expression. 52 . 2

A: Given, 52·2

Q: Set up the appropriate form of the partial fraction decomposition for the following expressions. Do ...

A: To find the value for the expression using partial fraction decomposition,                         ...

Q: Express the integral as a limit of Riemann sums. Donot evaluate the limit.  integral 2 to 6  x/(1+x5...

A: Given:               ∫26x(1+x5)dx   Expressing the Integral as a limit of Riemann Sums=?   Solution:...

Q: When you turn on a hot-water faucet, the temperature T of the water depends on how long the water ha...

A: When you turn a hot water faucet, we'd expect the temperature to keep increasing. But this temperatu...

Q: The graph of f shown below has vertical asymptotes at x = - 1 and x = 3. Find the following limits. ...

A: Since you have posted multiple subparts, as per our policy we will answer first three subparts. Plea...

Q: Integration by parts Evaluate the following integrals using integration by parts.

A: Given:              ∫1e2x2 ln x dx After setting dv=x2.dx and u=ln x for using integration by part, ...

Q: What consequence does the lack of uniqueness of polar coordinates have for graphing? Give an example...

A: To find the importance of uniqueness to polar coordinates

Q: Simplify: 9√(x)3.

A:

Q: simplify 1 53. x + 3 1 x - 9 54. x + x - 2 x - 5x + 4 2. +

A: 53 ) Simplify: 1x+3+1x2-9

Correlation

Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.

Linear Correlation

A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related. 

Regression Analysis

Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.