Let r(t) = (-5t¹-2, - 5e³t, 2 sin(3t)) Find the unit tangent vector T (t) at the point t = 0. Round to 4 decimal places. T(0) = Check Answer

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A: Given: Perimeter of the rectangle is 6x3+9x2-10x+5 and length is x.we need to find the width when…

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A: Let's find rate of change of blood pressure.

Q: (2x+5)³(52²-2x) 4. Use logarithmic differentiation to find the derivative of the function y = √2x+5

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Q: S √x²-a² X dx

A: To solve the given integral.

Q: Find fxy(x,y) if f(x,y) = (x5+y³) 7. fxy(x,y) =

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Q: Find the tangent plane to the equation z = - 3x² + 2y² + 4y at the point (4, 1, - 42). 2 = Check…

A: I am attaching image so that you understand each and every step.

Q: Problem Set #1. (w/Answer Key) 1. x²y' = x²+1 3y² +1 1. y(y² + 1) = (x² + Cx - 1) X

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Q: A company produces two types of solar panels per year: x thousand of type A and y thousand of type…

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Q: 1.5: The area of the region enclosed by the graph of f(x)=√x and the x- axis on the interval [0, 4]…

A: To find area

Q: S (2x² + 1) dx x3 - 3x +2

A: ∫2x2+1x3-3x+2dx This can be written as  ∫2(x2-1)x3-3x+2+3x3-3x+2dx=2∫(x2-1)x3-3x+2dx+3∫1x3-3x+2dx

Q: Determine the common ratio r, the fifth term, and the nth term of the geometric sequence. 4 8 16…

A: We know that the nth term of a geometric sequence is given by  a·rn-1 where a is the first term and…

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Q: Allouette Shipping Company has a peculiar fee schedule. When determining the price to ship a…

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Q: Q4. Find the values of the constants a, b, c so that F = (axy + bz3³)ī+ (3x² - cz)j + (3xz² - y)k is…

A: Note: According to our expert guidelines only first individual question is to be answered kindly…

Q: For each of the following, use the table of integrals found in the textbook to find the an…

A: Answer is in next step. please give a like !!

Q: Find the volume of the solid bounded by the elliptic paraboloid z = 1+ 2x² + 5y², the planes * = 5…

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Q: Pls answer fast 2+2

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Q: 8. Find the stationary points of the following functions and classify them as relative maxima,…

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Q: Find the gradient vector field (F(x, y, z)) of f(x, y, z) = ln(x + 5y + 6z). F(x, y, z) = =

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Q: Find all the values of x such that the given series would converge. ∞ (-1)" Σ (x¹)(n+3) (5)" n=1 The…

A: answer is in next step. please give a like !!

Q: = Approximate the area under the curve y with 4 subdivisions. x³ from x = 2 to 4 using a Right…

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Q: Find the center and radius of the sphere with equation (z + 3)² + (y + 1)² + (z+4)² = 1 Center:…

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Q: In the figure, the regions A, B, C and D bounded by the x-axis and the graph of f have the following…

A: Here we will find the definite integral,

Q: A spherical iron ball 8cm in diameter is coated with a layer of ice of uniform  thickness. If the…

A: Given data:- The diameter of the iron ball is, 8 cm The thickness of the coating is, 2 cm The rate…

Q: SEND IN 20 MINUTES PLEASE !!!! Find the absolute max. and absolute min. values of f on the given…

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Q: Find the absolute maximum and minimum, if either exists, for f(x)=x² - 6x + 6. Find the first…

A: We have to find absolute maxima and minima of given function.

Q: of the function given by the equation derivations details.

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Q: 1. Conisder the vvf r(t) = 12ti — +8t³/2 j + 3t² k, t> 0. (a) Find the arc length of the curve for…

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Q: Determine whether the following vector field is conservative on R³. If so, determine the potential…

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Q: Find the area under the curve y Т over the interval [1,4]

A: Topic = Area

Q: ✓cos x lim x 0 1 cos x - -

A: The given limit is limx→01-cosx1-cosx

Q: (b) Sketch, on separate graphs, each of the following functions (ii) sech(x). (iii) coth(x).

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Q: Find d dr (73 (7²). Type In(x) for the natural logarithm function.

A: As we know that; The Power law: ddxxn=nxn-1 And the common derivative; ddxlnx=1x   Let, y=7x

Q: Find the area of a triangle PQR, where P = (-4, -2,-2), Q = (-5, 2, 5), and R = (-2,5,-4) Check…

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Q: A company manufactures mountain bikes. The research department produced the marginal cost function…

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Q: + y² x² + y² = 64 from x=-1 to x=-3 Find the length of arc of the curve x²

A: Given: x2+y2=64 From the limit  x=-1 to x=-3 To obtain the length  of the arc:

Q: 4. Let f(x, y) = y²exy (a) Find the normal vector to the graph of f(x, y) at (0,1,1). (b) Find the…

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Q: 2- The circle ² + (y-2a)2 = 4a² is rotated about the line y = -1 where a > 0. A torus is obtained…

A: Given: the circle x2+(y-2a)2=4a2 is rotated about the line y= -1 then torus is obtained from this…

Q: Evaluate f 4x²-3x+2 X dx.

A: Given, ∫4x2-3x+2xdx

Q: Let f be a continuous function such that 10 1 of f(x) dx? 4 What is the value of 4 8 f(x) dx 10 1²°…

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Q: A body of mass 4 kg is projected vertically upward with an initial velocity 34 meters per second.…

A: Solution is given below:

Q: Evaluate the integral by interpreting it in terms of areas. 4 to −9(1 − x) dx

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Q: Find the following limit. lim

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Q: S XP al dv (v-1) (v +3) (v-Y

A: We are asked to evaluate the integral.

Q: Suppose that f(x, y) = 5, and D = {(x, y) | x² + y² ≤ 1}. Then the double integral of f(x, y) over D…

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Q: find the area of the region enclosed by the curve defined by y=x^(2) -2x-15 and the x-axis. Please…

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Q: 5. (a) Suppose a particle moves along a trajectory given by the vvf r(t). If its veloc- ity and…

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Q: Match each equation in rectangular coordinates with its equation in polar coordinates. x² + y² = =…

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