5. S 2x' dx 6. S*-5x* dx x3

Q: ||r(t) × r"(t)|| ||r(t)||* Use the formula k(t) to find k(t). r(t) = 4 cos(7t)i+4 sin(7t)j+ 3tk K(t)…

A: By using the formula kt=r't×r''tr't3 to find kt.rt=4 cos7t i+4 sin7t j+3t k

Q: Find the arc length of the graph of r(t) = ev2ti+ e¯v2tj+ 2tk, 0<t < v2 In 5 NOTE: Enter the exact…

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Q: Use the Root Test to determine the convergence or divergence of the given series or state that the…

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Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

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Q: Suppose the function f is continuous on the closed interval (1, 2], f(1) = 5, and f(2) = 9. Then,…

A: Intermediate value theorem: if “f” be a continuous function over a closed interval [a, b] with its…

Q: ||r'(t) × r"(t)|| Use the formula k(t) to find k(t). 3 r(t) = e"i+ etj %3D K(t) = ||

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Q: Evaluate the limit tan x lim z0 2x

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Q: Ley y = tan x. (a) Find the differential dy. dy = (b) Evaluate dy and Ay if x = t/3 and dx = -0.1.…

A: (a) Here f(x)=y=tanxdy=f'(x)dxdy=sec2xdx    =sec2(π3)(-0.1)    =-0.4

Q: Find the arc length L of the graph of r(t). 1 r(1) = r} i + t j+ Vor² 2<t< 5 L =

A: We need to find arc length.

Q: Dix) is the price, in dollars per unit, that consumers are willing to pay for x units of an item,…

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Q: is said to be the Laplace transform of f, provided that the integral converges. to find L{f(t)}.…

A: Let's find.

Q: Determine equation of the line in vector form, parametric form, symmetric form and scalar equation…

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Evaluate the integral. 3 if -2 < x< 0 f(x) dx where f(x) | 4 – x² if 0 <x< 3

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Q: Find the arc length of the graph of r(t) = ev2ti+ e¯v2tj+ 2tk, 0<t< v2 In 5 NOTE: Enter the exact…

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Q: Suppose that f is a continuous function such that = -12. Find xp (r)f P(*") dz.

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Q: 64 8 If f is continuous and f(x) dx = 18, find xf(x²) dx.

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Q: Example: Find C² sint]? Solution:

A: To solve the following problem

Q: Find the cost function for the given marginal cost and fixed cost. See Example 8. Marginal Cost…

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Q: Find a power series representation for the function. (Center your power series representation at x =…

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

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Q: In constructing an open rectangular box from 48 ftf of material, what dimensions will result in a…

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Q: (a) Determine the Cartesian equation for the parametric curve defined by x(t) = 5 sin t and y(t) =…

A: We have to find the equation of the curve ,tangent equation to the curve.   Note - As per our…

Q: Find the limit. NOTE: Enter the answer using round brackets. t² + 4 1 lim t→+∞ \ 8t2 +9' 4t |(?, ?)

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Q: Calculate the derivative of y with respect to x when sin(x + y) = 6x + 4 cos(y). (Use symbolic…

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Q: Determine whether the sequence is convergent or divergent. If it converges, find the limit. {n² tan…

A: Here we have to check the convergence of the sequence.

Q: st Show all -. If s = 1+3i, t = 2 – 5i and u =– 2+ 5i then calculate your working. Write your answer…

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Q: Evaluate the limit sin 3x lim 9x

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Q: 3 2. (8x2 – 3x) (12x2 – 3) dx

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Q: am dA y² dx + x² dy = / / ( - əx ду for the given path. hC: rectangle with vertices (0, 0), (2, 0),…

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Q: A Triangular number counts the objects that form an equilateral triangle. The nth triangular number…

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Q: Recall that csc(x) and cot(x) = sin(x) cos(x) sin(x) d4 cot(x) The ratio dx csc² (x) is a constant…

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Q: The function f(x) : 2x3 – 27x? + 84x + 8 has one local minimum and one loca This function has a…

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Q: Let f(1) = 5I + 2. Using the definition of derivative at a point, %3D a. enter the expression needed…

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Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

A: r(t)=cos(πt)i-ln(t)j+t-12kDomaincos function takes all values  ie  -∞,∞logarithmic function takes…

Q: a · Va? +1 dæ: 3 Consider the indefinite integral This can be transformed into a basic integral by…

A: We have to find the given integral.

Q: ||r(t) × r"(t)|| Use the formula k(t) to find «(t). r(t) = e*i+etj K(t) =

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Q: Graph the feasible region. x + y 2 3 -x + y 2 1

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Q: sin x dx 1. V2-cos2x

A: integration

Q: Find the area of the region under the graph of f on [a, b]. f(x) = x2 - 8x + 20; [-1, 2]

A: The detailed solution is given below Thank you

Q: Q2) Convert the polar function r tan20 to cartesian. %3D

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Q: 10 9. Consider the function f(x) %3D Let F(r) be the antiderivative of f(z) with F(1) - 0. Then F(x)

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Q: Q9. Find the equation of the tangent plane to f(x, y) = x In(y) + x²y+3 at the point (x, y) = (2,…

A: Consider the equation of the form          F(x,y,z) =0 then the equation of the tangent plane to the…

Q: Write the standard form equation for a hyperbola with center at the origin, vertices at (0, 6) and…

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Q: Find the particular solution of the following ODE given that y(0)=0 and y'(0)=3: d'y dy +10 +25y = 0…

A: Explanation of the answer is as follows

Q: 4. Find the indefinite integral. (Remember to use absolute values where appropriate. Use C for the…

A: We have to calculate indefinite integral ∫{(3x2+6) /(x3+6x) }dx Let us say  I = ∫ {(3x2+6) /(x3+6x)}…

Q: f(x, y) = ln(x + y)

A: for the first order partial derivative we have to find fx = derivative of f with respect to x fy =…

Q: Find an equation of the plane. The plane through the point (7, 8, 1) and with normal vector 3i +j -…

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Q: 7. The ellipse with the equation y2 = 1 is rotated about the x axis to form a solid shape. A…

A: Given:  An ellipse:x252+y242=1  , rotated around x-axis. A cylinderical hole of radius 2cm along…

Q: The demand curve for a certain product is given by p(q) = 517- q. The supply curve is given by p(q)…

A: We have to find the consumer surpless.

Q: Police use the formula: v = /20L to estimate the speed of a car, v, in miles per hour, based on the…

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