f(x) = (–9æ² – 8)*(6æ² – 4)° f' (x) =

Q: 1. If f(x) cos(t) dt, then f'(x) =

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Q: 3. Find fz and fy where f(x,y) = In(x + y²).

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Q: Find the second partial derivative for the function z = x7-7xy + 6y2 with respect to x.

A: Solution of given question is written in below steps.

Q: dx Evaluate f- +1) using the Cauchy principal value.

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Q: For f(x) = e+cos(x), calculate f (0) by using the chain rule!

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Q: sin(t) dt , 1-4x 1+ t2 4 If f(x) then f' (x) =

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Q: Q5/ Determine the total differential If Z = f(x,y) = x²y², x=2rcose, y = 2rsine

A: Here, the total derivative rule used is: z=f(x,y)=x2y2 & x=2rcos θ , y=2rsin θ

Q: eralvate s Ēodp where C is represientee ぐ F (Xっy)= yi 土 6+) = 28ti + tj

A: To evaluate: ∫CF.dr→F→x,y=xyi^+yj^rt=28ti^+tj^ ,     0≤t≤7

Q: Example H·W: for f(x,y) = cos(xy) - x3 + y compute fxyy, fxxyy

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Q: Q5/ Determine the total differential If Z = f(x,y) = x²y², x=2rcose, y=2rsinė

A: this is a problem of differential. Based on the general formula and concepts we will answer the…

Q: xyz 3. If f(x, y,z)= In| +e 2 find f,, f, and f..

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Q: Assume that f(x) is a differentiable and invertible function so that f(3) = 4 and f'(3) = .…

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Q: 3 36 Consider a fumetion f whose first and second derivatives are f'(x) and f"(r) = 5/2 (1r² + 1)"/2…

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Q: (b) Integrate f(x, y) = 4e0.8x - 0.5y using h = 0.5 with y(0) 2 from x = 0 to 0.5.

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Q: (b) Find the first order partial af and ду af Əx ay for the derivative f(x y) = 2x² sin(x+ )…

A: To find the df/dx of partial first order differential we differentiate function with respect to x…

Q: Find the linearization L(x) of f (x) = tan x at a =

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Q: 3. Find the linearization L(x) of the function at a. F(x) = Vx, a = 4

A: Use the formula for the linearization of a function about any point.

Q: (b) Find the first order partial derivative af and for the function f(x, y) = x/y –x²y+ y²

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Q: Q3: Use Chain Rule to differentiate the following functions 1. f(r) = (4x² - 3r + 2) 2 2. y = csc(4…

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Q: f(t)=cos(at). f (t) = 2cos(3t). f(t)=1-cos(wt) f(t)= 4t · -f(t)=e.

A: Given,     1.  f(t)=cos(at)

Q: Find the linearization L(x) of f(x) = cot(x) at x = π/4.

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Q: B. Let z- ( x-y)exy Show: Zxx + zyy + e x9 Cy 3- x³)- -z (xy+ 2)

A: Given that                       z=(x-y)exy

Q: [16.46° At 377 A=-0.25+ j7.9852 Stable -0.1693 -0.50

A: We will discuss how lambda is calculated. Lambda is the eigenvalues. I will show you how lambda is…

Q: d) The function +(xy)-r*r2y) exp G 18xy is homogencous in of degree X and

A: The given function is: f(x,y)=(x2+2y)e2xy+8xy...(1) The function f(x,y) is said to be homogeneous…

Q: Find the partial derivative. z = (2² + 2x – 6y)"

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Q: a) z=-3x y² + sen(x²y) 2x c) z=-In (x y³) e) z = x²ln(2x³y) b) w=2xz-3e²xy d) z=2e²y sen(x) f) z=…

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Q: Find the linearization L(x) of f(x) = cot x at x = 4

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Q: - Find the total differential df of f (x, y) = (x² + y²) 3/2.

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Q: For the function f (x,y,z,w) with x, y, z, and w all functions of s, t, andr, write out the chain…

A: The function is fx,y,z,w x,y,z,w are functions of s,t,r.   Partial derivative of a function with…

Q: Find the zeYo k its ovdev for Sunction f2)=1-Ti + Z+ e.

A: Given the function, f(z)=1-πi+z+ez. Now, in order to find the zero of the function f(z), we will…

Q: lim, - „f(x) = 0, then fx)dx diverges Select one: O True False

A: The given statement is

Q: lim, f(x)= 0, then | f(x)dx diverges

A: Statement:  limx→∞ f(x)≠0,  then ∫1∞ f(x) dx   diverges.

Q: d Use the chain rule to calculate f(x) if f(x) In (1+ tº) dt. dx, 0. f(x) =

A: let's use chain rule and find derivative of integral.

Q: 39. (a) Show that 1 1 > 0 2x V1+x² for x > 1. (b) Use your result in (a) to show that 1 dx 1+x is…

A: The compleet solutions are geven below

Q: Q1) suppose that W= x2+y2+z² and x cos 0, y = sin0, z = tan 0 ,use the chain rule to find de when 0

A: We have, W=x2+y2+z2 and x=cosθ, y=sinθ, z=tanθ  We have to find, dwdθ=? at θ=π4

Q: df Find dx by using chain rule if f = u =-1 , x=-1 u+1

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Q: dy -x²()+5y= e3X +cos 2x is The ODE: X dx 3 dx Linear of order 4 Non-linear of order 3 Non-linear of…

A: If a differential equation when expressed in the form of a polynomial involves the derivatives and…

Q: 11) Find a function y-f (x) that satisfies both conditions: d - 6x -4x+5,f(-1) =3 dx %3D dy 2 3 ==+…

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Q: [4xy + 2x] 5) Let F(x, y) =[ 2x² + 1 Is F conservative? If so, give a potential function for F. %3D

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: ← Z 3 Z (ancosno) z (ansinno) = z (z-a cose) Z-2axwoso ta azsing Z² 2ax cose + a²

A: Introduction: Z-transformed is significant transformation in mathematics. In many fields, it has…

Q: Ôz 12. If z = cos(x y)+ y cos x , where x=u +v and y=u-v use the chain rule to find and ди

A: Given: z=cosxy+ycosxx=u2+vy=u-v2 Recall the chain rule,  ∂z∂u=∂z∂x·∂x∂u+∂z∂y·∂y∂u…

Q: 2 Integrate the function f(2) = (z - 10i) from z = 0 to z = 5 + 5i along the line x = y.

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Q: If z = xy2 + 6x, then y2 + 6 is the first order partial derivative of z with respect to x. O True…

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Q: Q9. Find y2 using Reduction of Order y" – 3.ry +4y = 0, Yı 1 = x?

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Q: If X and Y have the joint pdf fxx(x. y) 20sx<ys 1 fr(1/2) = fxpy-1/2(1/6) P(0<X<1/8 Y-1/2)

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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.