Find an equation of the tangent plane to the given parametric surface at the specified point. r(u, v) = u2 i + 9u sin(v) j + u cos(v) k;    u = 2, v = 0

Q: A spherical balloon is being inflated with helium at a rate of 201 cm³/min. How fast is the…

A: topic - application of differentiation

Q: Evaluate the geometric series or state that it diverges. 9e² 27e³ 64² 5127³ 3e 1+ + 8 + Select the…

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Q: Write the equation in logarithmic form and solve for x. (Round your answer to three decimal places.)…

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Q: Evaluate the integral: 2₂4-2² J O*[] π 2 [1-4] 021-]+0 O O 4T e4 dydx -√4x² ex²+y² +C

A: To evaluate the following integral.∫-22∫-4-x24-x2 dy dxex2+y2

Q: Given the hyperbola with the equation equations of the asymptotes. 22 4 y² 49 = 1, find the…

A: We need to find vertex, foci and asymptote.

Q: cy that best fits the data points (0,

A: z = a + bx + cy bx + cy + a = z Data points => (0, -3, 0), (4, 0, 0), (3, -1, 1), (1, -2, 1), and…

Q: Some ecologists divided a female bird population into three categories: juvenile (up to 1 yr old),…

A: We have to find the population of birds.

Q: Question 5. 56 The inverse Laplace transform of s² + 64 is Asin(bt), where A and b are constants…

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Q: 37-44 (a) Find the vertical and horizontal asymptotes. (b) Find the intervals of increase or…

A: Since the student has posted many sub-parts of the question and does not mention any specific part,…

Q: 5. Use the figures to calculate the left and right Riemann sums for f on the given interval and the…

A: Solution: Given function, f(x)= 2/x + 2 ,[1,5] n =4

Q: he table shows values of a force function f(x) where x is measured in meters and f(x) in newtons.…

A: Solution:

Q: Problem 7. series converges or diverges and mention the test you are using. Show all work. ∞ (b)…

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Q: Let f(x)=√8-x³¹ for x <2. -3.x² 2√√8-x³ (a) Show that f'(x) = - for x < 2. The graph of y=f(x) is…

A: Given a function y=f(x)

Q: Calculate the double integral SSR (2x + 8y + 16) dA where R is the region: 0≤x≤ 4,0 ≤ y ≤ 1.

A: The given double integral ∬R2x+8y+16dA, where R is the region: 0≤x≤4, 0≤y≤1. We have to evaluate…

Q: The total costs for a company are given by C(x) = 1,650+45x+x², and the total revenues are given by…

A: The costs for a company is given by Cx = 1650+45x+x2 The total revenue is given by Rx = 130x To…

Q: Chapter

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Q: Problem 6: Find the point (x,y) with x > 0 and y> 0 that lies on the curve y = 2x² and produces the…

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Q: Use the divergence theorem to calculate the flux of the - vector field F(x, y, z) = x³i + (8y −…

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Q: f(x) = 2x² + 2x + 1 (a) h(x) = lim h(x) = X→ 00 (b) h(x) = = lim_h(x) = X→ ∞ (c) h(x) = lim h(x) 818…

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Q: the a

A: The solution provided is correct.

Q: Problem 7: Find the derivative of each of the following functions. 2t (a) g(x) = f*2 2 + dt fx² -2…

A: if h(x)=∫axf(t)dtthen h'(x)=f(x)dsinxdx=cosxdxndx=nxn-1

Q: Why does I1 = ln(u) in step three?

A: We have to tell why does  I1 = ln(u) in step 3

Q: tch the graph of y=tan(x) for one cycle.

A: we will plot the required graph.

Q: 7. In the influenza pandemic of 1918–1919 about 40 million people died worldwide. A study in 2007…

A: Find the Local and global maximum and minimum values of D over the given time period and estimate…

Q: Find an equation of the hyperbola that has vertices (0, 3) and foci (0, +4). Equation: = 1

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Q: find an intergrating factor of the n for the equation form y t 2 (y² + 4xy) dx - x ² dy=0 hence…

A: Note : Since you have posted multiple questions, we will provide the solution only to the first…

Q: 29. [(5x-7)-² dx = k(5x-7)¹ + [√x+1dx=k(x + 1)/² + C (4-x)-¹ dx = k ln 14-x|+C 30. 31.

A: Given problems:- 29.  ∫5x-7-2dx=k5x-7-1+C 31.  ∫4-x-1dx=kln4-x+c

Q: re4 1 2 e² x ln²√x dx

A:

Q: A ball thrown in the air has a velocity of v(t) = 98 32t ft/sec at time t seconds. Find the total…

A: given velocity is  v(t)=98-32t   given  t=1 to t=8 formula used is  v(t)=ds(t)dt∫xndx=xn+1n+1+c

Q: Solve the FIRST ORDER LINEAR D.E. Linear in r sin 0 dr de = -1 - 2rcos 0

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Q: If a 180-mile trip took 7 1/2 gallons of gas, how many miles can be driven with a full tank of 14…

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Q: D.E Linear in y y' = x³ - 2xy → when x = 1, y = 1

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Q: please.   The rate of U.S. per capita sales of bottled water for the period 2007–2014 could be…

A: Given query is to find the total water sold in 2 years.

Q: 4.42. Evaluate Jcz dz+z²dź along the curve C defined by z² + 2z2+z = (2-2i)z+(2+2i)z from the point…

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Q: Assume that and y are both differentiable functions of t and are related by the equation 7- cos (62)…

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Q: 2. Building X is 100ft tall. Building Y is 200ft away from building X, where the distance is…

A: We can solve the given problem by using the trigonometric formulas.

Q: Problem 7. series converges or diverges and mention the test you are using. Show all work. ∞ (2) Σ…

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Q: find the area that is bounded by the curve ? = √(10sin(theta)) and lies in the sector 0 ≤ theta ≤ pi

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Q: If the two adjacent sides of a rectangle are always on the legs of a triangle, what is the length of…

A: let longer side of the rectangle = xlet shorter side of the rectangle = y

Q: Problem 7. series converges or diverges and mention the test you are using. Show all work. 00 (2) Σ…

A: To solve this problem we can use p-test , comparison test and root test

Q: 4. y(2xy² − 3) dx + (3x²y² − 3x + 4y) dy = 0

A: Given differential equation y( 2xy2 - 3 )dx + ( 3x2y2 - 3x + 4y )dy = 0 standard form Mdx + Ndy = 0

Q: Calculate the integral approximations T6 and M6 for ₁x¹ dx. Your answers must be accurate to 8…

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Q: Which interval is f increasing when f'(x) = x³ - x? (a). (-∞,0) (b). (-1,0) (c). (-1,1) (d). (0,0⁰)

A: we need to find out the intervals where function is increasing.

Q: 1-4 Find the local and absolute extreme values of the function on the given interval.

A: To find the local and absolute extrema for the given function

Q: 1. Determine whether the following series are convergent. If convergent, find the sum. A. B. n=1 1…

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Q: 4) 1z In 4

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Q: 7 п 11. 6 12. п

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Q: Solve the two (the first one using integration by partial fraction and the second using integration…

A: Question 1,Given,            ∫3x3x+2+4x4+2x2dxTo find : Solve using partial fraction.

Q: A consultant estimates that the total weekly computer usage by the company employees to be:…

A: Given query is to find the computer usage for first 14 weeks.

Q: Given that cos 0 = sin 20 = cos 20 = 60 and sin 8<0, determine the values of the sine and cosine…

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