When h(t) = 7t + 3t – 2, evaluate h( – 3) - h( – 3) =

Q: Q2: Given X =t +2x- +3u ди Find Xe 2

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Q: If Fx) is an antiderivative of x2 +x1, then what is the value of F(1) - F(-1)? 3

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Q: 7. Find c such that f(c) = fave where fave is your answer to the previous problem.

A: (7) The function is given as , fx=x3 find c for fc=fave where fave is average value of f on 0,27.

Q: Q3): If x fx + yfy = nf show that x²fxx + 2xyfxy + y² fyy = n(n – 1)f %3D

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Q: -2xy 3) y' = iy = -5 when x = 2 Ans: exact; x²y + y = -25

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Q: Differentiate H (w) = 2e"² - 1+w² •

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Q: d x3 in terms of t.) X1 + 0.5x2 + 0.33x3 + 0.25x4 0.5x1 + 0.33x2 + 0.25x3 + 0.21x4 = -1.7 0.33x1 +…

A: I have used MAPLE Software .

Q: (2) y" (t) - cy'(t) + gy(t) = 6t²²t where: you) = Y(u) =

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Q: If f(x, y) = 2x+6 (2a-6y) of then is given by:

A: In the above question we will take y as constant since we have to partially differentiate it with…

Q: d²y 54. Let y = 4r+2r+l_find CL)

A: To find the double derivative of below expression.

Q: FInd the implicity differentiate x^2- 4xy + y^2= 4

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Q: Calculate y*)(0) for 0 < k < 5, where y = x* + ax³ + bx² + cx +d (with a, b, c, d the constants).

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Q: -6t 3t2 7 Find i (t), given 7(t): %3D - 6t2 3' 3t3 2 3t F(t)

A: Given

Q: For Vx 3 evaluate y when y = 4. 2

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Q: f(t)=t²(3-2t)³ at t=1

A: Given function: ft=t23-2t3 Find the value of given function at t=1

Q: Find antiderivate. for eaen fenction when C=0. a) 8x? b) x4 C) x2+ 6X-7

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Q: If f(x) = | V17+t³dt, then what is f(-1)?

A: Leibnitz Rule: Let f(x) be a differentiable function on closed interval a,b such that a,bare the…

Q: alla Find xy² R2² -dA, R= [0, 4] × [ - 2,2] x² +1

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Q: f (x) = x³ – 23 6x + 1. | e sure to verify the c

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Q: J 5(x) =-J5(x) ylgn O İhi O

A: We have to solve given problem:

Q: Let h(x)=−2x2+x+4x2+4x−1, what is h′(−5)?

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Q: Q1: 2ty 2t – (2 – In(t + 1)) y = 0 y (5) = 0 t2 +1

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Q: Q.2 a- If w=xy+ find y2 +1 a²w a²w and дхду дудх

A: Solution Part A  Given. w = xy+eyy2+1  We have to find ∂2w∂x∂y   and  ∂2w∂y∂x

Q: 2t + 7 f(t) = t- 3 %3D h(n) = - 2n2-3n+1 %3D f(h(-1)) =

A: Here we have two functions f(t) and h(n), we want to find the value of f(h(—1)). To find f(h(—1)),…

Q: 11. x = 2t – 2 and y = -t + 2 for 0 <t < 4 | Domain:

A: In this question we have to find the Domain.

Q: For Vx - 3 evaluate y when y = 4. O 4 O 4 O-2 O 2

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Q: Find by applying the chain rule repeatedly. y= (/2- 3x +3)? f'(x) =O %3D

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Q: If (x and jy)² = 3 + j8, find x and y.

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Q: Q3 Find f-(x) for the following : 1- y = Jx-3 2- y = (2x³ + 1)'/5

A: For finding the inverse, we will replace x with y and y with x

Q: 3 4. If y = t3 + 3t? and x = t - 8t2, show that y" = 16t(t+2)(t-2)3

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Q: (j) z = y² – x² + 2x - (k) x² – y² + z² + 4.x + 2y = 3

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Q: So (e2t + e-t)²dt

A: We have to solve

Q: r. = x (n) |1,

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Q: y"- 5y + 4y ez.

A: Use second order ordinary differential equation rules

Q: What is the antiderivative of f'(r) = - 4x + 3

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Q: Q14- If f(x,y) = 2xy - x² Iny- 2y² + 3x + 4, then axy is : for the function

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Q: - Q3): If xfx + yfy = nf show that x²fxx + 2xyfxy + y² fyy = n(n − 1)f

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Q: Is the equation t²y' (1) t + 4 - separable? y?

A: t2y't=t+4y2

Q: Find x (t) 5 (2)^- 2 Z ニ (Z – 2)²

A: Function: In mathematics, a function is a relation between two sets that relates each element of the…

Q: 1.3 Verify that f d = xp= x2V1+ x2 V1+ x² +c using the method you were taught in this course.

A:

Q: The discriminant of ax2 + bx + c = 0 is defined by_________.

A: The given equation is ax2+bx+c=0.

Q: Given the function C(n) = 3nt – 30n3 + 72n2 -

A: The given function is- C(n)=3n4-30n3+72n2

Q: For Vx - 3 evaluate y when y = 4. O 2 O 2 O 4

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Q: f) VaeA : 3BEB : (3a>b X at&<o)

A: The given expression is: ∀a∈A:∃b∈B:3a&gt;b∨a+b&lt;0

Q: Calculate h'(r) using the Product Rule if Mc)- (-3) (구+ ) = (2x – 3)(x² + 7) then h'(r) = ex' (x² +…

A: We will use product rule of derivative and comparing the terms with given terms of derivative to…

Q: Perform the following in fóy (2y2 -3y4, -1/2 -3/4 3.

A: We have to find the given integration

Q: Find d²y/dx2 for the followi f) x2/3 + y2/3 = 1 %3D ³ g) x + y = 16

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Q: Let h(x)=−2x^2+x+4/x^2+4x−1, what is h′(−5)?

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Q: 18.t2y′′−4ty′+6y=0,t&gt;0;y1(t)=t2

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.