f f Find Af = where f(r, y) = In (9r2 + 5y2 – 3r). %3D

Q: 1) f(x) = *+x*, r<1 x'+1 x21 df = ?, x1 dx a) f'(x) = %3! b) f'(1) = dx I = ?

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Q: function fo) = 7X1+10x10x3_4 Qn Antiderivative of fo) is F(x) = Axn+ Bxm, CxP+Dx: A= 710 %3D where…

A: Solve the following

Q: d"y Q5 dx * - 5 d³y +74 – 3y = 20 sin(x), y(0) = - 1, y'(0) = 2, dx use the method of Variation of…

A: This is 3rd order first degree non homogeneous ordinary differential equation.

Q: dz dz d For the function z= 4x° +7y+9xy, find dx' dy' ax2(-5, – 2), and dy 2(-5, - 2). dz

A: Consider the given function. z=4x3+7y2+9xy The objective of the problem is to find the partial…

Q: 3x sec (xy)dA; R={{x,y): 0 sxs7,0 sys 1}

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Q: Get z = f (x,y), x= e° cos t, y = es sin t Show that it's + ) - 2 2 =e 2s + əx. əs

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Q: dy at x = 2 for the function below. dx Evaluate у%3D — 2и + 4и + 9, where u %3D 4x2 — бх + 5

A: Given that,    y=-2u3+4u+9, where u=4x2-6x+5

Q: Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule t 4 10 In(x) dx, n = 6

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Q: | 9V In(x) dx, n = 6 (a) the trapezoidal rule (b) the midpoint rule (c) Simpson's rule

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Q: dx 2. Find the value of at y=1 if x=z³+4z and z= (y² + 2y)²/³. dy

A: We have to use chain rule while differentiating.

Q: 1 f =- хуz and evaluate it at x 1, y 1 Find dxdy dz2) and z = 1

A: Solution is given as below:

Q: 3xz dV where E: {(x, y, z) | 0 < r < 2, x < y < 2x, 0 < z < x + 3y} Evaluate E

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Q: 4 f:[0,00)→R all continious function aro Sx³f(x?)dx= Sx f(x) dx %3D show this.

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Q: find fy CX,Y) it (x,Y)=x2-8xy- 2y?

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Q: f(z) dr = 20 and f(1) dz = 3.1, find f(z) dz. %3D

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Q: 3zyz f(x, y, z) = e %3D fz fy = f =

A: The given function is f(x,y,z)=e-3xyz. Evaluate fx as follows. ' Thus, the value of fx is…

Q: Integrate f(x, y) = y(x² + y°)° over the domain æ? + y? 0.

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Q: dy Find given that dt dx x² + y? = 2x + 4y, x= 3 y = 1, and 7 dt dy i dt II

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Q: dy when t = 7. dx 13. Evaluate y = 2z? – 3z + 5 x = 4t' +t t = z? + z+1

A: Derivative of the function decides whether the function is increasing or decreasing. If the first…

Q: Find frx, fæy and firy for the function f(x, y) = (1+x + g)e*

A: Given: - The function is, f(x,y)=(1+x+y)e-xy To find: - The value of fxx,fxy and fyy for the given…

Q: f(r, y, z) = sec='(9x + 3yz) f. = fy = f; =

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Q: The integrating factor of + 2xy= 5x² is dx dy а. b. x? e C. 1 - d. et

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Q: f(x, y, z) = e-3zyz 三 fy = 三 ニ f.

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Q: Q 4. a) Use integration by parts to evaluate Sz²cos zdz. b) Evaluate f xlog(x + 3)dx.

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Q: 10 f(z) dz - f(z) dz f(z) dz where a = and b:

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Q: Exl. suppose the pdf of r.v. X is [x/8, 0<x<4 fx(x)= {*/8, 0<r<4 . Find the pdf of Y =-2X +8. 0,…

A: Y= - 2X + 8, we have dydx= - 2⇔ dx =-dy2and 0&lt;x&lt;4 ⇔ -8&lt;-2x&lt;0 ⇔0&lt;-2x+8&lt;8⇔…

Q: dz = 2ni to deduce that z+1 Use the fact that (x+1)dx+ydy Sc O (x+1)dy-ydx = 0 and Jc (x+1)²+y² =…

A: Given ∫c1z+1dz=2πi ......(1)we have to prove that ∫c(x+1)dx+ydy(x+1)2+y2=0 and…

Q: Hw z] Find Sxsin(x)dx using this rule.

A: Given that, Using the chain rule, The integral becomes,

Q: = [[ F - a5, I = S F = î4æz – jy² + kyz 1

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Q: fy = e*, y = 1 - e-x, and x = 0 ab- %3D

A: Given: - The curves of, y=e-x, y=1-e-x and x=0 about y=4.5 To find: - The volume of a solid is…

Q: Q.2 Evaluate dx. (i) Using Trapezoidal rule by takingh = 0.2, h = 0.5 & h = 0.25. %3D %3D

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Q: V Sove using variaton of parameters recuction of order or (D² - 2D+1) y = e*(e*+)*

A: Please find attachment for the details solution

Q: y2 f(x, y)dx dy Let f(x, y) = e-x2-y² and

A: answer is in next step

Q: S(r* +x )dx Approximate with n = 4 using Simpson's Rule Trapezoid Rule.

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Q: 2. CG X It otx

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Q: f(x) = 3x²+x+7. Approximate fo trapezoids. O a. 60 Ob. 44 Oc. 30 Od. 22 f(x)dx using the trapezoidal…

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Q: Find fr and fy for f(x,y) = I+y fz = /(r+y)? and fy = /(r+y)2

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Q: dz dz For the function z= f(x.y)= - 2x + 5y? + xy, find f, (5,5), and f, (5,5). dx' dy

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Q: cosh t f(x) dx = Choose... If S f(x) dx: = c, then 2f(x) dx = Choose... 9. S f'(t) dt = Choose..

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Q: r an antiderivative of f(x). Do not enter +cas ver: +c

A: topic:- integration

Q: Find (V.VxF), where F(x, y, z) = ln xî+exyzj+tan-¹ k.

A: According to the Bartleyby guideline, only one question can be answered. Please repost another…

Q: 4e4sin6x dx secбx Evaluate A) -In|sec6x| + C B 4sin6x + C 1 e4sin6x+ D 4In|sec6x| + C

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Q: 10 f(2)da - f(2)dz = /" f(x)dx f(x)dr %3D where a = and b = I %3D

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Q: af f f Let f(x, y) = x³ – 2.x³y + £y*. Find ²f and dx²' ay²' dx dy' ду дх

A: The function fx,y=x5-2x3y+12y4

Q: valuate dy and A v for v = f(y) = x2 -6x +35 x =4 and dy = Ax= 05

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Q: The antiderivative of [Vx-25 dx is V x2 - 25 - sec-x+ C. A True B False

A: Given: I=∫x2-25xdx     As we know from the trigonometric identities; 1). sec2x=tan2x+1 2).…

Q: jéäs) f(x) given below is concave-up Sx² + 1 : -1 < x < 1 1 < x < 3 f (x) .3 6x² :

A: We have to solve given problem;

Q: Q 4. a) Use integration by parts to evaluate f z²cos²zdz. b) Evaluate f xlog(x + 3)dx.

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Q: of of For the function f(x,y) = In (x+ 3y), find and dx df of ду II

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Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products. 

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.