Find r'(t). r(t) = (tan-(4t))i+t cos(t)j – Vtk NOTE: Enter your answer in terms of i, j, and k. r'(t)

Q: (cos(x)) dx cos(c) 3.

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Q: A plane is given by the equation 5x − 8y + 4z + 9 = 0 a. Find 3 points on the plane b. Find a…

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Q: no1

A: Topic:- application of derivatives

Q: If f(x) = (x2 + 5x + 8)*, then f'(x) = f'(5) =

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Q: 3 (a) | (7)dx (c) dx (sin x + 1)dx (b) L (x° + 2x + 1)dx (d) 0,

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Q: Evaluate the line integral, where C is the given space curve. y dx + z dy + x dz, C: x = t, y = t, z…

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Q: Solve the equation on the interval 0s0<2n. cos (30) = - 1 Vhat are the solutions to cos (30) = - 1…

A: We have to find the angle

Q: 2- A radio station conducts a poll about gun control. It invites listeners to call one phone number…

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Q: the comverg ence and divergene test 2n

A: To find the convergence of the series.

Q: Let F(x) = f(x*) and G(x) = (f(x)). You also know that a' = 5, f(@) = 3, f'(a) = 13, f () = 1 Then…

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Q: Q3 : prove that : cosh?x + sinh²x =coch2x

A: L.H.S.:=cos h2x +sin h2x=(cos hx)2 +(sin hx)2  =ex+e-x22+ex-e-x22=14(ex+e-x)2+(ex-e-x)2

Q: Find the area of the specified region. 5) Inside the limacon r= 8 + 2 sin 0

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Q: The arc y = x² from (0,0) to (2, 4) is rotated about the y-axis. Find the area of the resulting…

A: We want to find surface area

Q: Use the Shell Method to find the volume of the solid obtained by rotating region under the graph of…

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Q: -12 1. ("(25x – 46x + 3)dx -12

A: topic- definite integral if f(x) is a odd function∫-aaf(x)=0

Q: Find the Yalue + Cas

A: Using inverse trigonometric formula achieve this expression

Q: Consider the following. z = x2 + y2, x = 4s + 8t, y = s +t az az and as Find by using the chain…

A: Here, the given functions are: z=x2+y2, x=4s+8t, y=s+t So, z is a function of x and y and x and y…

Q: Use a Maclaurin series in this table to obtain the Maclaurin series for the given function F(x) = x…

A: A complete solution is given below.

Q: Find the absolute minimum and maximum value for the function on the given interval f (x) = x – 3x2 +…

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Q: 3 lim (1+ 4 x2

A: Given query is to find the limit of the expression m

Q: 5. Consider the region R in the plane enclosed by x-0, y=1 and y = x a. Draw the region b. Use…

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Q: Use series to evaluate the limit. X-In(1 +x) lim

A: Find your answer below

Q: Find the direction angle of v for the following Vel v = - 6i- 3j What is the direction angle of v?

A: On solving this we will get

Q: A farmer finds that if she plants 90 trees per acre, each tree will yield 30 bushels of fruit. She…

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Q: y = xx, x-4, nd y =0 Revolve the area of the shaded region about the line x-4. Using circular disk…

A: Given  y=x√x=x^(3/2) X=4 and y=0  Now volume of solid evaluated as  V=integration 0 to 4…

Q: Use the Ratio Test to determine the convergence or divergence of the series. If the Ratio Test is…

A: Ratio Test : Suppose we have a series  ∑ an.Define,   L =limn→∞ an+1an .The,(i)  If L&lt;1 then…

Q: Find the area of the shaded region. y y = x2 + 1 ... y = x -1 2

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Q: d Calculate ri(t) · r2(t)] and r1(t) × r2(t)] first by differentiating dt dt the product directly…

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Q: Suppose we want to evaluate the following indefinite integral -53z? + 98z +172 dr (z – 2){(7z + 12)…

A: Solving

Q: r0.5 .2 X- dx (lerror| < 0.001)

A: Given I = ∫00.5 x3 e-x2 dx =− ( x2 + 1 ) e-x220.50

Q: F. Change the Cartesian integral to polar coordinate 11-y !! (x² +y*)dx dy

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Q: Solve  x * (dy/dx) – x6ex = 4y

A: on solving this we will get :-

Q: 18. Find xV4x -3 dx 18. SxV4x - 3 dx

A: Use substitution to solve

Q: dy -1

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Q: Find (a) the critical numbers of f (if any) (b) the open intervals on which the function is…

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Q: Set up and simplify the surface integral ∬S F dS where F(x,y,z) = 2xi + yzj - √y k and S is the part…

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Q: TUTOR %3D for the function

A: The given equation is: 4x2+x3y+y2=6...(1) To find the slope, that is dydx, at Q(-1,2)

Q: Radius and Interval of Convergence of a Power Series. 00 Determine the radius and interval of…

A: Solve the following

Q: Solve y’’ – y’ + y = 2sin(3x)

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Q: Graph the problem and solve using vertical or horizontal rectangle. Show your solution. 1. Find the…

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Q: Question 2 x2 Consider the function f(x) = x² –1 " (a) Find the intercepts of the graph of f (if…

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Q: Determine the area of the gtven reglon. y = x + sin X Step 1 Note that for the glven reglon, x…

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

Q: 1) Find dy/dr by implicit differentiation. tan n'(xy"+y)= x

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Q: Use the chain rule to find the derivative of: cos(7 + 8x)

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Q: f4) = (/4x² +8 - x²)* (8x + 4x)V4x2 + 8 - 24x - 32x V4x2 +8 If then f'(x) =

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Q: Use the Taylor series for f(x) = Vx, centered at a = 16, to approximate the numerical value of v17.…

A: This question can be solved using the concept of Taylor series centered at a.

Q: nd lim l Nx-3 and simplifu X-79

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

Q: (-1) ntl n=1 n3

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Q: Find the arc length of the curve y = from x=2 to x=3 2x2 16

A: Use arc length formula

Q: Find the Maclaurin series for the function. (Use the table of power series for elementary…

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