Problem 3. evaluating them. 1 a) Lot (12 - 31³1/²2 S - dx Determine whether each integral is convergent or divergent by (c) for (b) for 1 X - - 3)¹/2 dx te-2t² dx

Q: a. Find a curve with a positive derivative through the point (1,1) whose length integral is given…

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Q: Determine if the following series converges or diverges. Indicate what test you use. a) Σ 1 2 n=1 n²…

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Q: Find the value of 3 sin(2x) sin(x) dx.

A: Given query is to find the integral.

Q: Consider the function f(x) whose second derivative is f''(x) = 3x + 8 sin(x). If ƒ(0) f'(0) = 3,…

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Q: Find the intervals on which​ f(x) is​ increasing, the intervals on which​ f(x) is​ decreasing, and…

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Q: 2 كل ك 0.5 , 3- = (f(x رشد -

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Q: Use polar coordinates to set up and evaluate the double integral f(x, y) = x + y, R: x² + y² ≤ 16, x…

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Q: (c) Find the value of √a²- [₁ 2(x+y) x² + y² giving your answer in terms of a. 1+ dx dy,

A: The given integral is  ∫0a2-x2∫-aa 1+2(x+y)x2+y2dx dy

Q: 34. S₁ x sin x cos x dx

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Q: Problem 5. they all start at n = 1. (a) an = (b) bn = 3n 1 + 2n (−1)n-1 5n List the first six terms…

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Q: (2n+1)! b) Ση=1 (3)η

A: Let us consider a series ∑n=1∞un with limn->∞un+1un>1 and also {un} is monotonic increasing…

Q: Calculate the gradient of f(x, y) = xy at (x, y) = ( − 1, - 2). Vf(-1, -2)

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Q: Convert the general form to standard form of parabola

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Q: If ƒ(6) = 7 and ƒ’(6) = 4, estimate ƒ(5.8). f(5.8) ~

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Q: Let [145 Find f(x) dx = 7, 13 + [1² f(x) dx = [ 11.5 and 11.5 $ 1.1³ 13 11.5 [ 7f(x) 6 dx = = f(x)…

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Q: The equation N (t) 550 models the number of people in a town who have heard a rumor 1+49e-0.7t after…

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Q: Determine the values of λ for which the system below has nontrivial solutions. (5-2)x-5y=0…

A: The given equations are; (5-lamda)x-5y=0 -3x+(3-lamda)y=0

Q: Use Laplace transforms to solve the initial value problem: y" - 10y' +9y = 5t, y(0) = -1, y'(0) = 2

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Q: Find the volumes of the solids generated by revolving the regions bounded by the graphs of the…

A: we need to find out the volume.

Q: 9. Find the distance between (1,) and (1, π). (a) (c) √2 √3 (b) 2 (d) √π

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Q: Find the most general antiderivative of the function. (Check your answer by differentiation. Use C…

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Q: Use implicit differentiation to find y′ for the equation below and then evaluate y′at the indicated…

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Q: 5e 42 sin(y), find a unit tangent vector to the level curve at the point component. Present your…

A: The function is  f(x, y)=-5e-4xsin(y)

Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. = $₁²04²…

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Q: 5 Find (7-2i) i=1 First write out the summation: Find the answer: Submit Question

A: Note : Since you are sending 2 different questions so as per policy I can solve only one question.

Q: A rectangular box which is open at the top has a height of x. The length is thrice its height, and…

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Q: 1. (a) (b) (c) (d) Find Maclaurin series for the function e-2x 2² 2³ 1+2x-x + _ 2! 22 2x+x 3! 1-2x²…

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Q: 8. Find the slope of the tangent line to the parametric curve x = 4 cos(t), y = 3 sin(t) when t=…

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Q: A farmer is constructing three equally-sized pens against the side of a barn for his animals, as…

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Q: Convert the following standard form to general form of parabola. a. (y+1)²=-2(x+2)

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: lim x -> 0 (3x * cot(3x)) . Do not use sing L'hospitals Rule

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Q: above by the surface Tuery² and below bu

A: We have to find the volume by double integration according to the given information

Q: 25-34 Use implicit differentiation to find an equation of the tangent line to the curve at the given…

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Q: = (-₁,3/-) ₁ a. Use the following definition of the slope of the tangent line at x = a to find the…

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Q: 15 4 12 x

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Q: 3). .Use the Comparison Test to determine whether the series converges. ∞     n = 1an where an =  2…

A: The given series is:∑n=1∞ an ;      where an=2n(n+4)

Q: Consider the following. 62 1 + ex (a) Find the exact solution of the exponential equation in terms…

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Q: Please show your answer to at least 4 decimal places. Suppose that f(x, y) = x³y². The directional…

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Q: Graph the following function and find the area under the curve on the given interval. f(x) =…

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Q: ху lim (x,y) →(0,0) x² + y² x²y lim 2 (x,y)→(0,0) x4 + y²

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Q: Problem 6. that the pattern of the first few terms continues. (a) { 1 1, Find a formula for the…

A: Given Sequence :- (a) 1,13,15,17,19,....... (b) 2,-43,89,-1627,3281,.....

Q: The profit P (in hundreds of dollars) that a company makes depends on the amount x (in hundreds of…

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Q: 2. 2 S² X (x + 1)² dx

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

Q: Solve the differential equation. sec(0) Be de dt

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Q: Find the first partial derivatives of 4xy f(x, y) 4x + y af dx = -(2, 3) = = af -(2, 3) : dy = at…

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Q: 7. Find the rectangular equation if r = 4 cos 0 + 4 sin 0 (a) (c) x² + y² = 4 x² + y² = 4(x + y) (b)…

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Q: g(x)= 4x ln x, find g’(x)

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Q: A water tank in the shape of an inverted circular cone has a base radius of 2 m and height of 3 m.…

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Q: 5. Graph by converting to exponential form first. You must graph at least 3 points. y = log ₂(x+4)…

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Q: Write an expression for the nth term of the sequence. (Your formula should work for n = 1, 9,8 +12,8…

A: Given sequence:- 9,8+12,8+13,8+14,8+15,......