Find the limit. (t i - 8 j+r k) lim t→2 lim t-2 (t i – 8 j + r² k) = i i+ i j+ i k

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A: Given dEdt=25-8t To find E(t):

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A: Note- I am answering the question as per diagram as further details does not mentioned in your…

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Q: Find the if yvx- 8 = xy + 2 Vx - 8 = xy + 2 – 8 dx

A: We can find the derivative as below.

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A: Given problem:- Find the average value of f(x, y) over the region R. f(x, y) = x R: rectangle with…

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Q: y a+h Figure 1.3.2: Plot of y = f(x) for Preview Activity 1.3.1. b. Construct a right triangle whose…

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A: topic- trigonometric functions

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A: We can solve as follows

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A: Given curvesy = 4x2y = x2+3

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Q: 5. Find the derivative if yyx – 8 = xy + 2

A: yx-8=xy+2Differentiate w.r.t x

Q: 1. Trace the curve whose equation is x* – x' y = -7x² + x+6 х* + 3х-10 Identify the following a.…

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Q: Please answer number 5. And how can we identify what kind of graph is that.

A: Topic:- function and it's curve

Q: 0.5 -5 -4 2 -0.5- -1.5 Find the following limits, if they exist. 3. lim f(x) X-3 4. lim f(x) X-2

A: We have to find the limit of the function by observing the given graph.

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Q: Find the average value of the function over the given interval. You must show your wo x2 - x +1 f(x)…

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Q: Determine the value of a, given that the line ax+y+1 = 0 is tangent to the graph of y= ax-6x+1 at x…

A: Given  y=ax2-6x+1find derivativey'=ddx(ax2-6x+1)y'=2ax-6+0y'=2ax-6at x = 1y'=2a(1)-6y'=2a-6

Q: 4) Find the equation of the plane that passes through the point (6,0, 2) and contains the line x = 4…

A: The plane that passes through the point (6, 0, 2) and contains the line x = 4 − 2t, y = 3 + 5t, z =…

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Q: 2. Evaluate the following definite integrals: S dx -22-x b. S32 sinx dx а. С.

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A: Given that radius = 20 m. So, OA = OC = 20 m. Given OB = 10 m. So, BC=202+102=500=105 m.   Let, D =…

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A: We have to find ∫3x2 dx.

Q: ques

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Q: Test the series for convergence or divergence. E sin? n n+ 3n

A: Given

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Q: ii, Calculate the volume and surface area of a solid cylinder 1.5 m diameter and 2.5 m tall.

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Q: A car rental agency rents 210 cars per day at a rate of ​$40 per day. For each ​$1 increase in​…

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Q: 3) Which type of quadric surface listed in Table 2 below is 4x² + y² + 4z² – 4y – 24z + 36 = 0?

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Q: 2y edy S- e-1 y

A: We are authorized to solve only one question, please repost remaining questions Integration

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Q: Test the series for convergence or diverg-

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Q: Use the derivative to find the exact critical points and intervals of increase and decrease for f(x)…

A: 1. Local maximums and local minimum values2. fx=4x3-21x2-24x+5

Q: 7. Point P(-5,k) is on the terminal arm of angle 9 in standard position. If csc9: 13 then: 12 12 a)…

A: This question can be solved using the concept of relation between rectangular and polar coordinates.

Q: Rewrite the Cartesian equation x = 7y as a polar equation. r(0) = Use the math palette or type theta…

A: Solve the following

Q: 38. 4y" + 8y' + 3y = 0

A: Question no.38 solved

Q: Determine the number at which h(x) = V16 – x² is continuous. - Determine the largest interval on…

A: h(x) = 16-x2 here in root &lt;0 is not  possible so 16 - x2&gt; 0 x &lt; 4 for this value function…

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Q: Consider a triangle ABC like the one below. Suppose that B=75°, a= 68, and c=49. (The figure is not…

A: Cosine Law :       cos A = b2+c2-a22bccos B = a2+c2-b22accos C = a2+b2-c22ab

Q: a) Find the fifth term of the sequence 16 31 46 61 9' 15' 21' 27 b) Find the general term of the…

A: a)169,3115,4621,6127,....b)1010,1815,2620,3425,....

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Q: A tank of water in the shape of a cone is leaking water at a constant rate of 2 ft'/hour. The base…

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Q: Use the Product Rule to calculate the derivative for the function h(t) = (t² + 3) (t + 8) at t = 2.…

A: Product rule:d(uv) = u v' + v…

Q: Find the arc length of the graph of the function over the indicated interval. (Round your answer to…

A: Given functionf(x)=32x2/3differentiate w.r.t.xf'(x)=32*23x23-1f'(x)=x-13f'(x)2=x-132f'(x)2=x-23we…

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A: We have to find the absolute minimum value for the function  f(x) = x2 + 9x + 5.6  Over the interval…

Q: Determine the number at which h(x) = V16 – x² is continuous. %3D | Vx2 – 1 Determine the largest…

A: In these question , we can check where the function is continuous . Check where the function is…

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