2. Remy, a rat, is walking along a straight pipe. His directed distance (in inches) relative to the starting point at time t is given by R(t) = 2t³ — 15t² + 36t – 8. (a) At any time t, find his rate of acceleration. (b) Find the time to if to is the first instance that he changed direction. (c) At t = 1, determine if Remy is speeding up or slowing down.

Q: Evaluate: ƒ³₁ ƒ²₁ √√²[z³(x + y)³] dz dy dx

A:

Q: Evaluate the following Integral using integration by parts X CSC X S - dx CSCrCOU

A: Use by parts method of integration

Q: Find the solution of the given initial value problem. v- 7 y = y' cost t-7' y (π) = 0, t> 0 y(t) = =

A: The standard form of the first-order differential equation is: dydt+Py=Q Where P and Q is the…

Q: (5) If f(x) =........., then f(x) is reducible in Z5[x]. (i) x³ + 2x² + 2x + 1 (ii) x² + 1 (iii) x²…

A: This is a problem related to reducible and irreducible nature of the polynomial while in Z5[x].…

Q: 2 3) 9 = x ² sin x y વચ્ચે ઝ 4) y = sin x 1-2 cos x

A:

Q: Determine the roots of y"" - 3y" - y' + 3y = 0

A: The given differential equation is: y'''-3y''-y'+3y=0   So, we can also write as; D3-3D2-D+3y=0

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A: I am going to solve the problem by using some simple calculus to get the required result of the…

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A:

Q: Find the volume of the solid generated by revolving the region bounded by y = e-x², the x-axis and…

A: Given problem is :

Q: Find the area of the region above the curve y = x^2 - 6, below y = x, and above y = − x.

A: Given region bounded above by  y=x2-6  and y=-x  and bounded below by y=x

Q: What is the answer? Show your complete answer (with a graph) in a given-required-solution

A:

Q: 1. Solve the following Linear Systems of Equations by Gaussian Elimination: 2.) 3x + 3z = 0 2x +2y =…

A: On solving this we will get

Q: Example 1: Evaluate the integral: ₁²²=238+1² 2r-3 - 3x + 1 dx.

A: The given integral is (2x-3) /sqrt(x2-3x+1), limit from 3 to 5.

Q: find the solution of following differential equation using Laplace transformation. y" + 3y + 2y = ex…

A:

Q: (d) Give the local maximum and minimum values of f (x). Enter your answers in increasing order of…

A: Local maxima and minima and concavity

Q: Evaluate: ³₁₂₁(4x²y — z³) dz dy dx

A: The given integral is  ∫-13 ∫-24 ∫10 4x2y-z3dz dy dx

Q: Evaluate the integral: S2 S² sin (=) dt du π/2

A:

Q: (2) Z/(5) =....... (i) (5) (ii) 5Z (iii) {[0],[1],[2],[3],[4]}

A: We have to find the operation

Q: II. Minor and Cofactor 1. Find the cofactor of 6 in matrix D 9 8 4 2 7 -9 4 D: 6 -3 (8 9 3 323 32 2)

A: In this question we have to find cofactor of 6.

Q: Which of the following is true about the function a(x) = 21² +1-6 #-+-2 O A. a(z) has an infinite…

A:

Q: 3 Evaluate the integral: Soft²eu du dt

A:

Q: Evaluate the following * 5 Sa 4x - 1 In(4x - 1) 4 O II -dx + C 5ln(4x - 1) 4 + C 5ln(4x − 1) + C 4…

A:

Q: Find the area of the region bounded by the curves y = 1 (x+6)²¹ į, y = = 4 and the x-axis using…

A: Explanation of the answer is as follows

Q: Find the area of the region bounded by the curves 1 y 5, y = 4 and the x-axis using vertical strip.…

A:

Q: please do the second (b)

A: Let's find volume when rotated about y axis.

Q: from the date set, find the value of f(7) by use lagrang method X 3 6 9 11 y 12 13 14 16

A:

Q: (1) Let I be a proper ideal of the commutative ring R with identity. Then I is a ........ if and…

A: (1) we have to fill in the blanks Let I be a proper ideal of the commutative ring r with identity.…

Q: Evaluate the line integral y dx + xy dy where C' is the rectangle with vertices (0,0), (5,0), (5,4),…

A:

Q: | √x dx 1 + √x A. x-2√√x+2ln (1+√x) + C 3. x-2√√x-2 ln (1+√√x) + C C. x-2√√x+2ln (1+√√x) - 3+C D.…

A:

Q: 2 ³₁²₁²[z³(x + y)³] dz dy dx -4 J

A: In this question we have to solve the given triple integral.

Q: 3 By direct partial integration, Solve the following PDES 8- 8²u axdy = ceBX Cosy SXUCX,#) Ex u(π,…

A:

Q: Q4/Find the slope of the line 3x-4y=-8 and then find the distance from the point P(3,-2) to this…

A: Given Equation of line3x-4y=-8To find slope & Distance.

Q: The value of sin cos (x²+)+C C. cos (x²+)+C xp B. -cos (x²+)+C D. -cos (x²+)+C

A: Topic = Integration Correct option = B

Q: (3) If R is an integral domain has non zero characteristic, then Char(R)=..... (i) 5 (ii) 4 (iii)9

A: Option (i)

Q: Evaluate: (4x²yz - ) dz dy dx

A: Let,    I  =∫23∫-14∫10 (4x2yz - z44) dz dy dx           I = ∫23∫-14[∫10 (4x2yz - z44) dz] dy dxI=…

Q: x = e¹0t y = t³ Which integral gives the arc length of the curve over the interval from t = a a to t…

A:

Q: Solve the general solution of the following linear differential equation: (y-cos²x) dx + cosxdy = 0

A: Given (y-cos2x)dx+cosxdy=0To find general solution:

Q: CSC X csc x - sin x - dx

A:

Q: It is given that the radius of the semicircle increases at the rate of 0.5 cms -1 when heated.…

A: Given ,  The radius of the semicircle increases at the rate of 0.5 cm s-1 when heated We have to…

Q: Find the area of the surface obtained by rotating the curve y = cos(2x), 0≤ x ≤ π/6, about the…

A:

Q: Consider the parametric curve: x = sin² (t) y = -9t Which integral gives the arc length of the curve…

A:

Q: Find the solution of the given initial value problem. y = ²7y= y' cos t t-7 Y(T) = 0, t> 0 y(t) =

A:

Q: • show that Ф (x, y, z) = 8²4 PDE: агф + дуг дуг х2 +у2 + Z2 8²4 872 satisfies the

A: First we find the respective partial derivative then add them to get value 0. see below the…

Q: 2. I. Evaluate each determinant. -4 3 -3 2

A:

Q: 4. The value of fx sin(x²+3) dx Acos (x²+) + C C. cos (x²+)+C B. -cos (x²+)+C D. -cos (x²+) + C

A:

Q: (b) Find the number c that satisfies the conclusion of the Mean Value Theorem for this function f…

A: This is a problem related to derivative. Based on the general formula and concept of mean value…

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A:

Q: II. Find the inverse of each matrix. 5 -11 1. -7 -9

A: This is a problem related to matrix. Based on the general formula and concept we will find out the…

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A:

Q: What is the equation of the tangent line to the curve y = at point (0,0)? O none of the choices O y…

A: Tangent line