find Fourier series an [o, 2] ○くxく下 f cx) = てくXく 2π

Q: Use the properties of the derivative to find the following. r(t) = ti + 4tj + t?k, u(t) = 4ti + t²j…

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Q: Find T(t) and N(t) at the given point. r(t) = 3 cos(t)i + 3 sin(t)j + tk; t = T .2. NG) = .2

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

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Q: Sketch the region enclosed by the curves and find its area. y = cos 4.x, y = 0, x 8' 4 NOTE: Enter…

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Q: Find the limit. lim (ti – 3j + r² k) 1-2 lim (t i – 3j+r k) = i+ j+ i k %3D i

A: The question can be solved using the concept of limits.

Q: Use a triple integral to find the volume of the solid. The solid bounded by the surface y = x' and…

A: Solution:

Q: If e is an angle in standard position, Cot(@) > 0 and sec(e) <0, then the terminal side of 0 lies in…

A: Trigonometry

Q: Find the volume of the solid generated by revolving the region bounded by the graphs of the…

A: Solving

Q: V4-y? cv8-x²-y² Use cylindrical or spherical coordinates to evaluate the integral. JoJ Vx?+y? A 32…

A: To find the value of the given integral.

Q: Use double integration to find the volume of the solid bounded by the paraboloid z = 9x2 + y?, below…

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Q: Find div F and curl F if F(x, y, z) = xz*i+ 6y°x*j+4z²yk. %3D div F= curl F=

A: To find the divergence and curl.

Q: Question 14 Find the area of the surface that is generated by revolving the portion of the curve y=…

A: Given: y=x2⇒x= ±y Since , we are dealing with x=1 to x=2, we will take the positive value Thus, x=y…

Q: Find the volume of the solid that results when the region enclosed by the given curves is revolved…

A: We have to calculate volume of solid obtained by revolving the region enclosed by curves x=cosecy,…

Q: 2 1 Evaluate the iterated integral. J J. J. (x² + y2 + z?) dx dy dz -1°0 A) 5 B 3 8 D) 10

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Q: 4 – X - 2 2 sin(x) |dx V 1 + x

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Q: Find fr(t) u(t)] and fr(t) x u(t)] in two different ways. r(t) = cos ti + sin tj + tk, u(t) = j + tk…

A: Vector

Q: Find the area of the region(s) enclosed by the curve y= |2x-6|, the x-axis, and the lines x =0 and x…

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Q: Question 8 Find the area of the region(s) enclosed by the curve y = |2x - 6|, the x-axis, and the…

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Q: 1- Show that the following subset is a subgroup. H = {o e S, l0(n) = n}cS,

A: We have to show given subset is a subgroup.

Q: Determine which value best approximates the area of the region bounded by the graphs of f and g.…

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Q: Find the area of the region bounded by the graphs of f (x) = x° and g (x) = Xx. A 1 в) 4 0.5 D 3

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Q: Question 17 Find the area of the region(s) enclosed by the curve f(x) = x°, the x-axis, and the…

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Q: Example 6 Video Example 0 A particle moves along a line so that its velocity at time t is v(t) = t2…

A: Given;  v(t)=t2-t-12.

Q: The point P(8, - 10) is on the terminal side of an angle e in standard position. What is sec(e)?

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Q: Find the approximate area under the curve of f (X) =cos ( from x =0 tox=T, Using 4 trapezoids. 3 2.6…

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Q: NC2)=

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Q: 1 Find the length of the arc of y= from x = 1 to x = 3. 2x

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Q: Find the directed distance from the given line to the given point. (-1, 6) (5, 4) (10, 8) (1, 2)…

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Q: Find the curvature and the radius of curvature at the point t = 0. %3D = e' cos(t), y = e' sin(t), z…

A: Given

Q: Find the volume of the solid that results when the region enclosed by the given curves is revolved…

A: Volume

Q: Question 20 Evaluate JJ xy dA , where R is the region in y = x? R (A) 13/7 (в) 16/3 18 D) 20 2.

A: We have to find the area.

Q: x Sin ( 3x- 2 |

A: Given: ∫ xsin3x-2dx   So, =-13xcos3x-2-∫…

Q: Find the conservative vector field for the potential function by finding its gradient. h(x, y, z) =…

A: We have to find the conservative vector field.

Q: Use the shell method to write and evaluate the definite integral that represents the volume of the…

A: We have to find the volume by shell method.

Q: Evaluate the iterated integral. x dz dy dx 128/15 16/89 23/6 6.

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Q: 4 y=V4x- 2/2x

A: Topic = Derivative

Q: 27х3-8а3 y3= y= 3x-2a Зх-2а

A: Y'=?

Q: A property has been mapped, and the height above sea level is determined to be represented by the…

A: Given a scalar field representative of height.

Q: find the differential dy. Hence, estimate the value of 1+ (1.023 2H y =

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Q: If 0 =. then sec(8) =1 (Write your answer in the simplest form, use fractions whenever applicable

A: Explanation of the answer is as follows

Q: Using Sandwich Theorem 3n2 + 1 an = (-1)" n³ – 4 converges to 0 O converges to -1 O none of them O…

A: We have to find the limit by using sandwich theorem,…

Q: Find the area of the region using a double integral. The region bounded by y = 4x°, 2x + y = 6, and…

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Q: Consider the following. f(x) = x* – 4x² g(x) = x² - 4 (a) Use a graphing utility to graph the region…

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Q: Which of the following angle measure (in degrees) is coterminal to an angle of measure 660 degrees?…

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Q: The population of mosquitoes in a certain area increases at a rate proportional to the current…

A: We have to find the equation of population.

Q: 1. Use the midpoint rule with n = 6 to estimate the value of the integral (x + x)dx. (5 points) 2.…

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Q: Question 15 1-sine Evaluate the iterated integrals J. J. p2 cose dr de̟ A 1 В) 2

A: ddθ(sinθ)=cosθ ∫rndr=rn+1n+1, for any real number n.

Q: Describe the graph of the equation: r = 5ti – 8j + (1 + 5t)k. [Choose the correct answer.] O The…

A: Given, r= 5ti -8j +(1+5t)k Therefore, The equation is given by, r= &lt;0,-8,1&gt;+t&lt;5,0,5&gt;

Q: Find an equation of the tangent plane to the surface at the given point. f(x, y) = Y, (1, 5, 5) %3D…

A: Given problem:- Find an equation of the tangent plane to the surface at the given point.   f(x, y) =…

Q: Write a definite integral that represents the area of the region. (Do not evaluate the integral.) Y1…

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