Use series to evaluate the limit. 4 3 sin(2x) – 2x + lim 4/3

Q: Find r'(t). r(t) = (tan-(11t))i+t cos(t)j – Vik

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Q: Find V x (V x F) if F(x, y, z) = 2:xyj+ 9xyz k. V × (V × F) %|

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Q: Answer the following True or False: Let f(x) be a differentiable function, such that f(– 1) = - 5…

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Q: 24) Identifa tue internel of convergen ce of a power ser's Ž (3)" n-1 (-3)", n=) a ) b) c) d) 3 2x23…

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Q: dt 1-cos t+sin t

A: First we shall simplify the expression then integrate

Q: Find the sum of the series. 1 - In(4) + (In(4))² _ (In(4))³ 2! 3!

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Q: Find div F and curl F if F(x, y, z) = xz°i +2y°xj+62

A: Given: Fx,y,z=xz6i+2y8x2j+6z2yk

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Q: ||r(t) × r"(t)|| Use the formula k(t) to find k(t). %3D 13 r(t) = ti + t5j K(t):

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Q: 12) find the indefinite inteyral Inv dv 6 v3 Answery a) -L (2invtl /Ac 12 v2 bり- りよemvtiリ+c (2 12v2…

A: The given integral is ln(v)/(6v3).

Q: Find V (V x F) if F(x, y, z) = 8 sin xi + 6 cos(2.x - 3y)j + 7zk. %3D | V. (V x F) =

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Q: Find r'(t). r(t) = (tan-'(9t))i+t cos(t)j – Vēk NOTE: Enter your answer in terms of i, j, and k.…

A: We can solve this as follows:

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

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Q: sketch the given region R and then find its area. R is the region bounded by lines y=x, y=-x, and…

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Q: Determine if the following series converge: 2.4.6 . · (2n) ... (a) (b) ) Inn 3.6 - 9 · · · (3n) ...…

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Q: A ball is thrown into the air and its position is given by h(t) = - 4.3t2 + 41t + 15 where h is the…

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Q: Problem 11. Solve the following system and express your solutions (if any) as individual ordered…

A: 3x2-2y2=-5     2x2+4y2=18

Q: Find the absolute maximum and minimum values of the function on the given curve. Function: f(x. y) =…

A: Let's find.

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

A: This question can be solved using the concept of domain and of functions and value of a function at…

Q: Consider the initial-value problem y" + 4y = 5 sin 3t, y(0) = 0, y' (0) = 3. %3D (a) Use the Laplace…

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Q: dx cos4 6x

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Q: Determine the vactor feld of F. F(z, y) = yi - j

A: This is a problem related to vector field calculation. Based on the general concept we will provide…

Q: Find r'(t). r(t) = (tan¬(11t))i+t cos(t)j – vtk NOTE: Enter your answer in terms of i, j, and k.…

A: Here, the given vector function is: r(t)=(tan-1(11t))i+tcos(t)j-tk

Q: -2- At the point shown on the function above, which of the following is true? O f' > 0, ƒ'' > 0 Of'…

A: If the second derivative is positive then the graph of the function is concave up.

Q: dx sinxtanx

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Q: 9) use the snell metnod to sef up end eveluete tueinteyrel tret gives the volume of the solid…

A: Using shell method, volume is evaluated.

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

A: Vector

Q: . Tind the general solution of the given variable separable can ation. O 20oSx dx - 3sinx Siny dy =0…

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Q: S-2 ds (s-1)(s-5)(s+3)

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Q: Consider the function f(x) = 5 – 4x² , – 4 < x < 2. - The absolute maximum value is and this occurs…

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Q: Find r'(t). r(t) = (tan '(7t))i+t cos(t)j – /tk NOTE: Enter your answer in terms of i, j, and k.…

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Q: Problem 5 Part 1: Consider a cost function where C(x) in Philippine peso is the total cost of an…

A: Let's find.

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

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Q: Use series to approximate the definite integral I to within the indicated accuracy. 1/2 x arctan(x)…

A: We have to find the value of integral.

Q: Answer the following questions for the function f(x) = x/x? + 1 defined on the interval – 5 <x < 7.…

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Q: Find r'(t). r(t) = (tan-'(11t))i+t cos(t)j – Vfk NOTE: Enter your answer in terms of i, j, and k.…

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Q: Consider the function f(x)=−3x2+30x−2.   a.   ​Determine, without​ graphing, whether the function…

A: Given; f(x)=-3x^2+30x-2

Q: Use the formula k(t) ||r(t) × r"(t)|| to find «(t). %3D r(t) = t²i + t°j K(t)

A: We have to find the value of k(t).

Q: Find div F and curl F if F(x, y, z) = 17y*z*i – 3x'2ºj – 3ry®k. div F= curl F=

A: Let's find.

Q: 4. x(x² – 1)² dx

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

Q: Evaluate the area of the region bounded by y2 = x and y2 = 6−x.

A: To find : Area between y2=x and y2=6-x First let's find the intersection points x=6-x⇒x=3 Therefore,…

Q: S V9x² + 64

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Q: Find curl (8z i + 9x j+ 10y k). curl (8z i + 9x j+ 10y k) (i )i + ( i j + ( )k

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Q: S(Vcos x + sin x)´dx

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Q: Given f"(x) = 7x – 3 and f'(-2) = -6 and f(-2) = 6. Find f(4) %3D |

A: Here we will find f(4),

Q: 1. The approximate value of -31.8 using linear approximation O -2.0025 O None of the choices O…

A: Ni

Q: Given: z = a' + æy", r = uv² + w®, y = u + ve" az Find when u = 2, v = – 3, w = 0 dv

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Q: Find the second and third derivative of the function (a) f(x) = x6 – 3.x5 – 41x – 73 - |

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Q: t3 – 7t2 + 16t –- 12 t4 – 4t3 + 4t² 5. lim t2 w? – 4w + 1 6. lim w-00 3w2 + 7w – 4

A: limt→2t3-7t2+16t-12t4-4t3+4t2

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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