Use the Comparison Test to determine whether the infinite series is convergent. ∞     k = 3 sin8(k) k8

Q: What is the equation of a parabola that passes through the points (-5, -10), (-3, 2), and (2, -3)? O…

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Q: The value of the following limit is -1 None Undefined 0 1 +∞ fin(n+¹) coth x dx limn→+∞ Jin n

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Q: Evaluate the definite integrals (show your solutions) sẽ có cos³ 3xsin3xdx

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Q: State where the power series is centered. Σ n = 0 (-1)^(x-4)2n (2n)! Submit Answer

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Q: ) Obtain the differential equation of the family of plane curve described and sketch at least 5…

A: We have to find the differential equation of the family of plane curves, that is "straight lines…

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Q: 2. x² dx |x2+16

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Q: Find the equations of the tangent and normal to x² - y² = 7 at the point (4, -3).

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Q: f(x) = 4x√√√2x² +1

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Q: Write the differential dw in terms of the differentials of the independent variables 7x+y u+z…

A: Let's find diffential dw in all other term given.

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Q: Find lim (1+ I-X 4 T

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Q: 6. Convert: a) Coordinates of point D(-1,-5) to polar coordinates, r> 0 and 0 <0<2n.

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Q: Use a geometric series or the nth-Term Test to determine the convergence or divergence of the…

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Q: Determine whether the function's vertex is a maximum point or a minimum point. x² + x + 2y = 7 O The…

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Q: 6 S(2 − |x + 4|) dx 3

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Q: A person drinks a cup of coffee. Assume that the caffeine enters his bloodstream immediately and…

A: The half-life formula is given by, f(t) = (Amount of caffeine initially) [1/2](t/(t1/2)) where t1/2…

Q: Question Three (a) Prove that F(x, y, z)= (y² cosa+z³)i+(2y sin a-4)j+(3rz+2)k is a conservative…

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Q: List the first five terms of the sequence. an = cos(n) 1 a2 a3 a4 a5 || = || = =

A: We have to solve given Questions.

Q: mange the point (-2,2, from rectangular to cylindrical coordinates and spherical coordinates. √²-25²…

A: Given ;  Point = (-2,2,1).

Q: The side of a cube is measured to be 21 cm, with a possible error of cm. A. Use differentials to…

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Q: Atmospheric pressure P in pounds per square inch is represented by the formula P = where is the…

A: Topic- Functions We are given P=14.7e-0.21x Where P is the atmospheric pressue in pounds per square…

Q: 3 Given the function of f(x) = -1 + on the interval [-8, -2], find a point c between -8 7x and-2 so…

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Q: Find the general lower and upper sums (in terms of n) of the area of the region ba g(y) = -8y over…

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Q: raph of the function f(x) = x³ + 2x - 1. So, the point (2,1) lies i (f¹)'(2). (Here f-1 denotes the…

A: Given query is to find indicated function.

Q: Which of the following is equivalent to 2x + 5 S (2-4x) 5 after appropriate algebraic substitution…

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Q: Determine the vertex, pocus, directrix and axis of symmetry of the parabola with the given equation.…

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: question 18

A: We need to find dimension of fencing.

Q: Calculate the directional derivative of f(x, y) = x³y² in the direction of v= 2i - 2j at the point P…

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Q: 3. The area of a circle increases at a rate of 47 cm²/s. How fast is the radius changing when the…

A: We can find the required answer in the below steps using the given data.

Q: 1. xe3xdx

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Q: 5. Find the least and greatest distances from the origin to a point on the circle (x - 1)² + (y −…

A: We know that circle equation is - (x-h)2 +(y-k)2 = r2. Here (h,k) is centre of the circle and r is…

Q: A box with a volume of 8m³ is to be constructed with a gold-plated top, silver-plated bottom, and…

A: Given:         Assuming the box is a cube.         The volume of cube = side³           side3=8…

Q: (d) Give one example to illustrate that vectors satisfy the triangle inequality. Justify your…

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Q: The area of the rectangular piece of cardboard shown below is 198 square inches. The cardboard is…

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Q: Given the following graph a. Evaluate f (3). f(3) = Number b. Solve for f(x) = 3. n ril H Submit…

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Q: In step 3, how did you know to use yp = ( 1 / (D^2 + 9) ) 4sin(2x)?

A: The given initial value problem y''+9y=4sin(2x), y0=1, y'0=1. We have to find the solution of the…

Q: Find the critical point of the function f(x, y) C = == (7x + y² + In(√x + y))). Use the Second…

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Q: The weight of a lake trout as a function of age satisfies the formula where Wis in kg and t is in…

A: The weight of a lake trout as a function of age satisfies the formula Wt=241-e-0.22t3 We have to…

Q: Write each equation in polar coordinates. Express as a function of t. Assume that r > 0. (C) x² + y²…

A: NOTE: Refresh your page if you can't see any equations. . use the cartesian to polar substitution…

Q: (a) Using algebraic division and integration by substitution, or otherwise, show that - dx = e² −…

A: We can evaluate the given integral by using the substitution u = ex

Q: S(2+ ex)²dx

A: ∫2+ex2dx

Q: (c) You are given the point (3, 2) in polar coordinates. (i) Find another pair of polar coordinates…

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Q: Find the average value of the function y = 35 - 2x on the interval [0, 4]. O 31 10 O 20 O None of…

A: The Answers are given below

Q: Apply the Second-Derivative Test to find all relative extrema of the function  f(x)=cosx-x ,…

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Q: Using test points from the original function give where the function is i 0x1 0x1 Ox>-3 Ox 1 x < 1

A: Solve this function by taking derivative greater than zero