Referto Forcion TOF nctior fCx)=X+4 (+) a cx)=2x²+2x

Q: 2. If F = (3x² - 3yz)i + (3y²-3xz)-(32²-3xy find div curl

A: Given problem:-

Q: * Evaluate. 2t |4 + et| dt

A: Solution :-

Q: Use Cramer’s Rule to solve x + 6y − 4z = 10 4x − y − 3z = −8 x + y − 2z = 7

A:

Q: (a) 3 Differentiate y= y 3= us ing first principle. 2x+2

A: we are allow to do one question at a time  if you rest of answere please specify that part and…

Q: ☺ cosh"z= Loy {2+/2

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Q: Qvestivr C-

A: question on co-ordinate geometry

Q: Obtain the general solution using variation of parameters y''+y = (csc³x) (cotx)

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Q: fxVx+ 6dx

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Q: method; Inz VUna)²-y²

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Q: Exampi r(x) = (/2x + 1 - x²)-1 %3D "(x) =

A: Given query is to find the derivative of the expression.

Q: iven by 5x3 at x = 1 is: %3D

A:

Q: Compate the Cantiderivative of fox) = x²+4 xナ4 %3D x³+ax

A:

Q: Differenitate: y = esin (z²+2z)

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Q: x = 4 y = x' |(2, 8) y = 8 y = Vx (4, 2) Figuro 1

A: Solution for question a: In figure 1 the region is bounded x=y2,the x-axis, where 0≤y≤2 The formula…

Q: | x(1 – x)193dx

A: Proceed as shown below

Q: X, t 2 X, < 22 X,t 3, 2x x, Z12 + 2xa=32 maxlimzed by 2=5x, t10x2

A: The solution of given linear programming is given by using graphical method :

Q: Evaluate the integral: dx 3xv4x2 –9

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Q: Find mZR. 2/2 mZR = %3D Submit

A: From the given figure:   With respect to ∠R   Perpendicular=QPBase=QR=2Hypotenuse=PR=22   From the…

Q: 5. y' = 2x?y – 4y %3D

A: 5 Given differential equation is y'=2x2y−4y......1. We have to find the solution of the given…

Q: Show that Live - de = In(V5- 2). -1 Vx2 + 2x +2

A: We need to show that, ∫-11-dxx2+2x+2=ln5-2

Q: Use the subst ition =x+y=0 4x-3y=0 By Your answer is

A: -x+y=0  -----&gt;14x-3y=0  -----&gt;2from equation1-x+y=0⇒y=xsubstitute y=x in equation 24y-3y=0y=0

Q: dv Integrate 9 + v2

A:

Q: b) Show that 2x² + 8x + 14 = 2 (x + 2)° +3 by completing the square. Hence, evaluate the integral-…

A: Use integration rules

Q: is Flaiy)= integrahing an 2

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Q: the of olution using simplex me Max z = 8x, + 10x, + 7x3 s.t: 4x + 6x3 + 3x3 S 60 7x, + 2xz + 5x, S…

A: In this question, the concept of Linear Programming is applied. Simplex Method An approach to…

Q: Consider (x8+ 8x5+ 16x2) ² -dx. Using u-sub

A: Given: - The integral is, ∫x2+1xxx8+8x5+16x22dx To find: - The values of k and n. By using…

Q: Sa x5 √x² + 1dx

A: To integrate.

Q: Solve for x: V3x +6 +V4x – 5 = 3 (4х — 5 3D 3 x= – 74+42/3 74+ 42V3 x = 74 – 42/3 x = 74 +42y3

A:

Q: 3)으 rcose de Jsine 1-x2 d ¿= xp 2

A: LEIBNIZ RULE

Q: Verify using Pathagoream Thereom EA 2xv x44 -radius

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Q: Use Cramer's rule and solve 6x-4z=26 7x+8y+5z=122 9x-9y=54

A: Use Cramer’srule and solve.

Q: 11 sec²(3t), 0 < t C₁ and C₂ as arbitrar

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Q: the 1) By uing of far 3 deliv ahve 3x at X-2 . %3D

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Q: 5lim V3+x-J3 8→0

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Q: Use Cramer’s Rule to solve:…

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Q: Evaluate. 2t 2t dt%3D

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Q: Evaluate the integral. r1/2 xp VZ14 SV16X2 - 1

A: From the given problem:   I=∫2412dxx516x2-1 .....(1)   Let,…

Q: SHOW 12 dzc= In (7+4V) 2. 8 Vx2 -8X

A:

Q: By applying product rule to find y' 3 (1+x*) x4 - x*

A:

Q: Use Elimiretion Methal 3x =38-4y 9x= 122-13y %3D %3D |

A:

Q: Solve Utt - c²uxx = 0, –n 0, %3D и(х, 0) %3D f(x), и(-п,t) %3D0 %3D и(п,t), и,(-п,t) %3D 0 %3Du,…

A:

Q: 38 Show that x² V2x – 3 dx - 35

A: use the formula below to evaluate the given integral.

Q: Use Cramer's rule to solve for y. 5x + 4y + 4z = 39 4x +3y-2z 15 4х - 5y - 4z%3D -15 |

A:

Q: b) Show that 2x2 +8x +14 2(x+2) +3 by completing the square. Hence, evaluate the integral dx. (x…

A: Given that: ∫3(x+2)2x2+8x+14dx

Q: O Express : 2 as a linear combination of

A: By using definition of linear combination

Q: Irr( V1 + 7, Q) = Vī, Q) = O gt – 4x² – 2 O xt – x - None O xt – 2x² – 6

A:

Q: Evaluate / lx+ v 49-x Jdx by interpreting it in terms of areas.

A:

Q: Eliminate the arbitrary conutantu 2. %3D y= ax + be

A:

Average

In mathematics, everyone must have heard the term average in one place or other. Almost all types of calculation require taking out an average. In everyday life, the term is used for denoting a certain amount that can be said to be a typical quantity for multiple people or objects. In other words, if a group of people possesses a certain object, then the average gives us an idea regarding the quantity of the object possessed by each person. However, this is solely based on mathematical calculation. It is important to note that most people will not strictly have the average value in a group.