-1 Vx? + y² dx dy+ | ] .2 .2 + y dx dy -2 -1

Q: d/dx (dy/dx)` x=1, , where y = x3 + 2x - 11

A: To find: The value of ddxdydx at x=1. Given: The function is y=x3+2x-11. Formula used: Power rule of…

Q: ● √3x dy dx √x² + y² So So

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Q: syidr + [2yłn () + 3siny]dy: 6. x²+3x 3y?dx 5x ;when x = 1, y = 0 x+3,

A: Given, Differential Equation:  3y2x2+3xdx+2y ln5xx+3+3 sin ydy=0when, x=1 and y=0 To find: The…

Q: 8. dy dx || = -X y

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Q: 5 (x² + y² )dx dy -5 J –1

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Q: dy Find for y %3D —8x csc-"(-6х) dx dy dx

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Q: Evaluate the integrals

A: ∫01∫0x2∫0x+y2x-y-z dz dy dx

Q: dy/dx - y = xy5 = 0 Ans. 1/y* = -x++ ce 4*

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Q: (у*- 2ху)dx + Зx*dy %3D 0 Nhen y 3D 1, х — 2 ||

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Q: H2. 2dy dy dr2 d²y dy :1 at x = 0. dx – 52+2y= 2x², y=7 and - dx

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Q: dy dr 1. cos(r + y) y(0) = 2. (4ry + 3x²)dx + (2y + 2r²) = 0, y(0) = –2

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Q: d'y dy -4- 4- dx? dx -3y=0. y(0)=1, y(0)=5

A: According to the given information, it is required to solve the given differential equation.

Q: dy y- dx2 dy dy = 7(y+1) dx? dx

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Q: 3 For y = 3x + x + 3 dy = -1 = dx

A: Given that:y=3x3+x+3To find: dydxx=-1

Q: y(2x? - xy + 1) dx + (x - y) dy = 0, ANS. y(2x – y) = c exp (-x?).

A: Given differential equation is y(2x2-xy+1)dx+(x-y)dy=0

Q: (2x + ) dx + ( – 2y) dy = 0 12. (2х + 1+x?y², 1+x²y²

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Q: dy is: 1 dx Given y = x²e_2x

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Q: 22 2 dy = 1-x +y _xy 2 2 x y dx

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Q: 6. f(x, y) dx dy

A: Double integration and area of integration

Q: 8. Find dy dx' x+2x given y = u³ + 4, u = .2

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Q: 3x dy 2y when x = 1, y = -1 dx 2y

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Q: 5 If y = dy then dx %3D x+1

A: Given that: y=xx+15

Q: dy - Solve + 3y + 2. y dx = x, given y (0) = 1. %3D dx

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Q: 2х-1 dy if y=f and f'(x)=sinx²,find dx x+1

A: According to chain rule of differentiation if f and g two functions are differentiable and function…

Q: Evaluate the integrals

A: The given integral is ∫02∫03y∫x2+3y28-x2-y2dzdxdy.

Q: d²y ex 1. Find dx2 for y = %3D (2x²–3)

A: According to our terms and conditions I have solved first question for next question repost

Q: dy y? – 1 y(2) = 2 %3D dx x2 – 1' -

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Q: dy/dx + 2xy + xy = 0 Ans. 1/y3 = -;+ 1 + ce3x? 2

A: The given differential equation is  dy/dx + 2xy +xy4=0

Q: 2. (2-x) dx + 2r y dy = 0 Ans.

A: As per our guidelines, we are supposed to solve only one question.Please repost the remainning…

Q: Find the first and second derivatives. -3 y = 5x - 11x -8x dy dx d°y dx? %3D

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Q: C. dy b. 4 sin 2x> , y = 2, when x = 2 %3D dx dy С. dx = x + 3+ e2x>, y = -1, when x =

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Q: •1 fl-x r4-x²-y 16. x dz dy dx 0 Jo 3

A: See the attachment

Q: 5/xy dy -2, х, у» 0 dx y =

A: See the details solution in below

Q: 1-y² V1-y? I-2(1- x) dy dx

A: We will divide and integral the given function

Q: dy %3D -9y = 0 with the conditions that x = 0 and dx

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Q: y = sinx + x² to dy dx? x² y +2

A: Given, y=sinx +x2 Differentiate two times with respect to x to get required differential equation.

Q: 1 Given y = 3x5 + -, dy is equal to 2x3 dx

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Q: Find dy/dx given that y3 + y2 − 5y − x2 = −4

A: We have to find dydx for given equation, y3+y2-5y-x2=-4 We know the formula from power rule of…

Q: dy اذا كانت y = 3z2 + (sin(z وكان = *3ez؟ 4 : أحسب dx

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Q: (у3 — у?sinx — х)dx + (3хy2 + 2усosx)dy %3D 0

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Q: 4. y dx -x dy = x + y? .2

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Q: 2x-1 11. y = 5x+2 12. y=(5x² + 2x + 1 )3 13. y = V2x + 6 /14. y = 15. x = 2x + 3, what is dy/dx? =…

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Q: Q3) (cos y – 2xy + dx – (x² + xsin y)dy = 0 x²+

A: Simplify the equations by grouping like terms and using the product rule of differentiation. Look…

Q: 1 -dy dx = 0 dy 2.xy- + y? – 2x = 0 | d.x

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Q: 1. ху' %3D у + уx? — у? d²y 2. х- dx² = 2-a dy dx 3. Зуу'у" — у'3 +1%3D0

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Q: d?y 7. y = e2" – 3e-, dx? dy - 2y = 0 dx

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Q: dy 2 ,? cosx +-y = -x²y dx %3D

A:

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.