6. Find the derivative of y= 2x² (3x - 4). A. 6x³ - 8x² B. 18x² - 16x 7. Find the derivative: f(x) = x sinx A. x\cosx - 4x3sinx B. x cosx + 4x³sinx C. 15x² - 6x D. 6x-4 C. 4x3cosx D. -4x³cosx

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A: answer is in next step.

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A:

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A:

Q: 2 /// }} لال ملاملا

A: The given equation is;  y'''-y''-6y'=ex.

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A: This is a problem related to graph function. Based on the general formula and concept we will answer…

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A:

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A:

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A: To solve a homogeneous differential equation of the form dydx=f(x, y), it is easy by making the…

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A: The objective of the question is determine the "yc".

Q: i/ - y - y - 6y = ex - الا و

A: Given

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A: This is problem of limit and continuity. Based on the general formulas and concepts we will answer…

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A: Given: y(3)-2y''+y'=1+xexAuxilliary equation: m3-2m2+m=0Therefore, m=0,1,1Complimentary…

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A: To find the area bounded first find the intersection of f(x) and g(x)

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A:

Q: Q1: solve the equations below: 1) S dx Jellt vast (1+

A: Given, ∫1x(1+x)2dx

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A:

Q: Provide your answer below: Domain in interval notation is Range in interval notation is

A: This is a problem related to domain and range of the function. Based on the general formula and…

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A: Let's solve integration by using trigonometric substitution.

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Q: For the function f whose graph is given, state the following. (If the limit is infinite, enter 'co'…

A: Given graph:-

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A:

Q: calculusssss please

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Q: a) 2x+3y-z-2 x-2y+3z= 13 4x + y + 3z = 9

A: Since you have posted multiple question in this question which are not interlinked so i have solved…

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A: Our Aim is to find the limit of the expression given below:-limx→∞x+2x26x-1-(i)

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A:

Q: 4) The area of the surface generated by revolving x= y²-1, 1≤ y≤ 2 about x-axis is S=...

A: To find the area S of the surface generated by revolving x=y2-1, 1≤y≤2 about the x‐axis.

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A: This question is indeterminate form of 1infinity and solved using L Hospital rule.

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A:

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A: Consider the graph

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Q: Give a general solution of the differential equation_D(D−2)³(D²+1)(D² − 5)(D² − 8D+19)² y = 0 .

A: Use the auxiliary equation  and homogenous differential equation.

Q: Evaluate cos¹3xdx. a. 0.245 b. 0.267 O b O d c. 0.229 27 d. 0.196 e. none of the choices

A:

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Q: given the following equation: 36y^2-4x^2=144.  a) determine if the function is an ellipses or a…

A: This question can be solved using the concept of conic section.

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A: To evaluate the given integral.

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A: Let's solve.

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A: Given: 6x186=0

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A: To find the differential equation.

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A: We have, y=ecos(x) We need to evaluate, y''+sin(x) y'+y cox(x)

Q: By using the unlimited coefficients method, choose the correct answer for this equation…

A: