d X 4 dt -x 1+t? dx

Q: dx = x(x – 1)(x + 1) dt has a solution that is (Select the correct answer)

A:

Q: 10. Evaluate: +4x dx (a) (b) (x2 -2x 4) dx (c) (t2-t) dt (et cos t) dt (d) dx

A: Here, we use the formula that integration of x^n is x^(n+1)/(n+1) as shown on board.

Q: dx + 3x = e dt -2t

A:

Q: d (F(x*) dt dx dx

A: Explanation of the answer is as follows

Q: If g(x) = - [e' - In(2t+1)]dt, find g''(x) . dx A e* -In(2x+1) 4 B (2x + 1)² 4 C (2x + 1)² 2 D (2x +…

A: To solve the following problem

Q: d | Vsint dt dx 3 2.

A:

Q: L[f(t)] = F(s) = [ e*“ f(t) dt -st

A: The given integral is a Laplace transform, it can be evaluated by the integral by parts method. Let…

Q: d & fle²- · *[e' – In(2t+1)]dt, find g''(x) . dx -2 If g(x) = - A B c) e*- D 4 et + (2x + 1)² e* -…

A: The Leibnitz rule for differentiation under integral sign is,…

Q: Integrate (a) S2(* dt (b) S(x+1)³ dx (c) cos(-x)(x²)dx

A:

Q: S f(t) dx = 0. 1.

A:

Q: dy 9. = 2+ e dt

A:

Q: Calculate the derivative.

A:

Q: 1 S(t – 4t) dt

A: Given that: The limit is limN→∞ ∑i =1N  iN2 - 4iN×iN .

Q: d Compute dx (1+t²)* dt x2

A:

Q: Sf(x) dx 5and g(t) dt = 4 %3D C.

A: The solution is given below

Q: d'y dy 4+y =r²-21 +3 dt? dt

A: We will calculate CF and PI separately then we will add them.

Q: D = d/dt, Solve dx/dt + 2x – 3y = 5t dy/dt - 3x + 2y = 2e2t

A: given dxdt+2x-3y=5t⇒D+2x-3y=5t   ...idydt-3x+2y=2e2t⇒-3x+D+2y=2e2t   ...ii multiply equation (i) by…

Q: Evaluate (for x>0) 3√x dt d dx A 2 1+t²

A: Given :ddx∫0x3dt1+t2

Q: 13 |X + 3 1 O A. [ at2 + bt + c° dt2 + et +f O B. at + b ct + d O C.[ at2 + bt + c dt + e

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: If g(x) = -S^*[e²− ln(2t+1)]dt, find g''(x) . dx 2 (A (2x + 1)2 Be* -In(2x+1) 4 (C) Ce¹+ (2x + 1)² 4…

A: Here is the solution of the given problem.  By using derives under Integral.

Q: dy 1 andy 3x? + 1 if- dx Find- atx = -1. dt dt 1 6 -6 ||

A:

Q: 1. F(x) = S t³ - 5t dt

A:

Q: d If g(x) = - S* [e'− ln(2t+1)]dt, find g''(x) dx -2 2 A ex. (2x + 1)² 4 (В B et + (2x + 1)² Ⓒe*…

A: Given that gx=ddx∫-2xet-ln2t+1dt

Q: Simplify the expression shown.

A: To simplify the expression ddt∫0t11+x2dx+∫11t11+x2dx

Q: t'dx -X X(1)= 2 dt

A:

Q: 4. F(x) = L*,(1 – t) dt %3D

A: Now , we will find the value of integration.  We know,  integration of  t.dt = t1+1 / 1+1  + C…

Q: .3 +3 dt dx X

A:

Q: xdx – Va² – x² dy = 0

A:

Q: сох3х S* (1/4 – 1) dt dx J3

A:

Q: s^2ds+2t(s+1)dt=0; s=0, t=1

A:

Q: 1) [ (2t–1)² dt 2 2 2) dx X 3) [ , x(x² + 1)° d.

A:

Q: d²y dy -4 dt? dt

A: given: d2ydt2-4dydt+5y=2et

Q: d. Evaluate dx dt (t2 +2t) -1

A: We use the Leibnitz rule of differentiation under integral sign to solve the given problem.

Q: t2 + 9 V8 - t dy if y = In dt Find dy dt

A: Given equation is y=lnt2+98-t. Compute the derivative with respect to t.…

Q: 4. Compute (a) 4 S"(3t2 – 4)z dx - dx 'x (b) x1+t² 4 dt dx -x 1+t2 d

A:

Q: .2 d Find dx 1 dt ở V1+t*

A:

Q: d (F(x^) = ew dt %3D dx dx

A:

Q: dx a. dt b. 2y dt

A: A)  given equation can be written as (D-5/2)X -2Y =0 -3X/4 +(D+2)Y =0  By using elimination method…

Q: dx = 1-t+ x- tx dt

A: Given, dxdt=1-t+x-tx to solve the given problem we have to integrate it with respect to t.

Q: So e(1+)t dt

A:

Q: の そ ニ ゼdd + とd dt :d と の まdと +(そ-乳)よy:。

A: As per the company's guidelines, we are supposed to solve first three sub-parts for you, kindly…

Q: ²+1 2e + t dt dx V4et – t² 2x

A:

Q: dxp. 2 25* * 50 dt |dx, dt 2 25 * - 25 *:

A: dx1dt=-225x1+150x2dx2dt=225x1-225x2s.t. x1(0)=25, x2(0)=0 We have to solve the above system for x1…

Q: 42. a. Find df /dx if f(x) = 2 In. dt. b. Find f(0).

A: Solution is given.

Q: 1- dt 2x 1 d Q10:- Calculate dt dx 2x 3- dx 'x SLn(t) dt. dx 'x

A:

Q: .2 dt t2 + 1 dx

A:

Q: d’y -4 dy +y=t²-2t +3 1. dt? dt

A: The given differential equation is; d2y/dt2 -4dy/dt +y=t2-2t+3. Repost the next part.

Q: 4 d 4. Find dx 2 Vt2+17 dt

A: The given integral is,

Q: 1 D. (a)S 3e3t dt

A: We have to find the integral

Q: 1? d²N dN – 2t-+ 2N =t ln t dt 2 di?

A:

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.