Given the vector function 7(1)=(31²-1, 1-8√F³, 12t-4), find the speed & arc length of the curve on the interval 1 ≤ t ≤ 4.

Q: Se (cot By 34 - πT) dy

A: On solving this we will get

Q: 4 Use technology to help you sketch the graph of each function for 0 ≤ x ≤ 27. a y=sin x by=sin 2x…

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Q: ♥ 82u = cos x cosy, u(x₁#) = X ₂ U (π, y) = 2 cosy 2 axdy Ans: u(x,y) = sinx sing + 2/2² + 2 cosy -…

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Q: Exercise (1-3): By Charpit method solve the following PDE

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Q: Q4: A) For each of the following ,find fx fy fex fyy fyx and fxy 2.f(x, y) = sin²(x-3y) 3.f(x,y) =…

A: Solution: The objective is to find the partial derivatives of the given functions

Q: In x -2 x dx

A: Given: I=∫12lnxx2dx   Apply the integration by parts to solve the given integral. ∫udv=u·v-∫vdu

Q: ∫ ln(1 + ?2) ?x

A: Let's solve given  integral.  We know there is x instead of ?.

Q: dx (x² +25)3/2

A: To find the integration.

Q: -1 7. S. ze³z² −1 dz Sydy .2 8.

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Q: Relative

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Q: classify the following PDES :- 827 827 дхг 82z =X+Зу +2 буду дуг 2 2 X ох Иxx - 2xy Иху +Ў Иуу X •…

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Q: H.W find the first four terms of the binomial series for the functions:- 4-(1+¹)¹/² 5-(1+x)*…

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Q: Find the vector 2u-5v where u = and v= Find the dot product of vectors p= and q = Q3: Find the unit…

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Q: b) Find the area between the 2 curves f(x) = x² + 4- 4x and x - axes and border with the two lines =…

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Q: A tank can be filled by one pipe in 6 hrs and by another in 8 hrs. If both pipes are open, how long…

A: Given problem:- A tank can be filled by one pipe in 6 hrs and by another in 8 hrs. If both pipes are…

Q: Find the volume of the solid obtained by rotating about the x-axis the region bounded by the curve y…

A: The volume (V) of a solid generated by rotating the region bounded by y=f(x) and the x‐axis on the…

Q: Suppose that P₂(x) = a + bx + cx² is the second degree Taylor polynomial for the function f about x…

A: We have to find the sign of a, b, c.

Q: 1. Find 2 numbers whose sum is 23 and whose product is a maximum. 2. Find the dimension of a…

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Q: The graph shown is f(x) = √√x + 2. 2 + X 54-3-2-1 1 2 3 4 5 -2- 3 What is the integral function that…

A: Using vertical strip

Q: àtics II, e the caraid Q3) By using the polar find region enclosed by y = x² and y = 1 Find the

A: Let's find region enclosed by curve and given line.

Q: Solve the given differential equation by using separable variables. 1. dy x-5 = dx y²

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Q: Stan77x dx

A: tan2x=sec2x-1

Q: I. A delivery rider is travelling along a horizontal line such that its directed distance from his…

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

Q: (6) _ z² = pqxy

A:

Q: 6. Set up the triple integral that will give the following: (a) the volume of R using cylindrical…

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Q: Solve the following integrals completely and honestly. Show your solution in ink and as neatly as…

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Q: The demand function for a firm's product is given by q = 18(3p, 2p)¹/3, where • q = monthly demand…

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Q: 3 Sketch the graph of each function for-27≤x≤2. a y sin (-x) by=2 sin (-x) cy=3 sin (-x) d Explain…

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Q: True False questions. Only need to answer T/F. Answer "F" if the statement is not always true. Here…

A: According to the guidelines, we are answering first three subparts. Please repost the remaining.…

Q: e for (2x + 1) cos(x) dx. 14. Use integration by parts to evaluate

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Q: 1. If A (in²) is the area of a square and s (inches) is the length of a side. Find the average rate…

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

Q: y = u√u-1 u = 2x² - 1

A: Given problem:- Find derivative  y=u√(u-1) , u=2x2-1

Q: 7. y"+y'+y=0 Ans: y=a*(Ccosx+Csinx) со

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Q: Let f(x)=sinx. Determine the x-value(s) where the function has a maximum or minimum value on 0,2m).…

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Q: Find Df,Rf/f(x). X 3 √x + √ X

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Q: 1. Find the area of the region bounded by the curve y=- 1+x² 2x² and the lines y = 0, y = x,x= 2.

A: First we draw the graph,

Q: Find the area of the surface obtained by rotating the curve from x = = 0 to x 5 about the y-axis. =…

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Q: 2. Given the values for f(x) on the table, approximate the area under the graph of f(x) from x = -5…

A: Let's find approximate area under the graph.

Q: ar the function A whose graph is shown, state the following. (If the limit is infinite, enter 'n'…

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Q: - 3)² = 81 then, find its ce or a=<3, -1

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Q: A В D ľ КIN 5л 2 (2 — 4sin(0) + 2 sin²(0)) d0 (2 - 4 sin(0) + 2 sin²(0)) d0 (1 — 2 sin(0) + sin²(0))…

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Q: 13. y = x², y = 0, x= 1; about the y-axis

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Q: What are the domain, range, and period of the function f(0) ) = -20cos( - 10) + 1₂

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Q: 2 [*x* (Inx)² dx

A: Given integration is evaluated.

Q: The radius r and height h of a cylinder are changing with time. At the instant in question, r = 4…

A: Given problem:- The radius r and height h of a cylinder are changing with time. At the instant in…

Q: A rectangular classroom has length that is 1 meter more than 2 times the width. Find the dimensions…

A: Given  Perimeter  of rectangle = 32m Now, let the length be 'L' and the width be 'W'. According to…

Q: let f(x)=x2 -9y  and  g(x)= √x. find the domain of (f o g)(x) and h(x)= 1 / (f o g)(x)

A: Let f(x)=x2 -9x and g(x)= √x. Now,        (f o g)(x)=fx                =x2-9x                =x-9x…

Q: Sketch and find the volume of the solid obtained by rotating the region bounded by the given curves…

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Q: Gradient 3. Find the gradient of the following scalar functions. (c) f(x,y)=at (-1.1) (d) $(x,y,z)=-…

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Q: Find the area of the region enclosed by the curves y = 4 24 8 0 16 x³ and y = 4x.

A: