Determine whether the series 2-√√n +∞o Σ √√n n=1 converges or diverges using the Integral Test.

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. =x²+²x≤x≤1 3x 2…

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Q: Find an equation of the line that passes through the point and has the indicated slope. Point Slope…

A: Given that , Point =-3,5 Slope m=-34 Find the equation of the line.

Q: ΣΕΠλη της 9 - 515 +1 _h=1

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Q: The Integral xy√√x² + y² dydx is equal to 1 Select one: O /(2√2+1) //(√2-1) 15 O /(2√2) /(2√2-1) O…

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Q: Find the equation of the tangent line to the graph of the function f(2)=√1026 +26 at the point…

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Q: Choose the correct answer by changing the order of integration of the following iterated integral…

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Q: Describe the transformations that map the function y=2^x on the function y=2^x+3

A: Solution

Q: Find all values of c such that fis continuous on (--,-). f(x) = {7-2², c=2.193 c= 3.193 7-2²³, xse…

A: The given function,    fx=7-x2,x≤cx,x>c

Q: What is the integral that represents the length of the curve from x 2 to x = 4. Select one: 4 ○ ₂²(1…

A: y = x4/4  length of curve formula  = ∫a b1+(dy/dx)2 here limit given from 2 to 4  a = 2  b = 4…

Q: The number of welfare cases in a city of population p is expected to be W = 0.006p4/3. If the…

A: We will apply the concept of implicit differentiation to solve the problem.

Q: Q4 (a) Calculate the surface integral: [] (² + (y² + 2yz) dS where o is the first octant of the…

A: To evaluate the surface integral Given plane 2x+y+2z=6

Q: Differentiate the following function: f'(x) = f(x) = e" + ce 니

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Q: Find F as a function of x and evaluate it at x = 2, x = 6 and x = 9. = $₁² F(x) = F(2) = F(6) = F(9)…

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Q: Find the second order derivation for y = e-3x².

A: d2dx2e-3x2

Q: Use a graph to find approximate x-coordinates of the points of intersection of the given curves.…

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Q: (a) Find the domain of the following function, giving you answer in interval notation. f(x) = ln(x²…

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Q: Examine the function f(x, y) = x³-9xy+y³ +8 for relative extrema and saddle points.

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Q: Draw a slope field for dy/dx= -6x^2/y.

A: we have to draw a slope field for dydx=-6x2y

Q: Find the Wronskian of two solutions of the differential equation t²y" - t(t− 3)y' + (t− 2)y=0…

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Q: What is the velocity of a ball dropped from a height of 150 m when it hits the ground? Take the…

A: The Solution is given below

Q: Evaluate the function at the given values of the independent variables. Simplify the results. f(x,…

A: Topic = Functions

Q: 20

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Q: Find ||FI|. F(x, y) = i + j Sketch several representative vectors in the vector field. y O O -4 -2…

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Q: Find the third degree Taylor polynomial T3 (x)centered at a = 1 for the function f(x) = 3 x²

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Q: The answer for x is correct but the answer for dy is wrong.

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Q: Find the absolute extreme values of the function on the given interval. f(x) = 9x³ - 108x on [0, 5]

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Q: Determine whether the series converges or diverges. n+5 Σ n = 11 (n + -6)5

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Q: Use Green's Theorem to evaluate the line integral. √y² dx + xy dy C: boundary of the region lying…

A: We have to evaluate the integral.

Q: The count in a bacteria culture was 300 after 15 minutes and 1500 after 40 minu count grows…

A: We will solve.

Q: Let f(x) be defined by f(x) = x² sin(x) + x³. Find f'(1). Note: Your answer (if it's not an integer)…

A: Please see the below picture for detailed solution.

Q: What is the area of a single right trapezoid? Note: in the formulas below, • L₁ and L₂ represent the…

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Q: Differentiate d/dx  ∫ [cos(x), 0] t dt (using the Fundamental Theorem)

A: Differentiate d/dx  ∫ [cos(x), 0] t dt (using the Fundamental Theorem)

Q: You're studying anacondas in tropical South America, and you've decided that a particular…

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Q: To determine drug dosages, doctors estimate a person's body surface area (BSA) (in meters squared)…

A: To determine the drug usages, doctors estimate a person's body surface area BSA in meters squared…

Q: 25. Find equations of all lines having slope −1 that are tangent to the curve y 1/(x − 1). = 1/4…

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Q: At the beginning of an experiment, a scientist has 160 grams of radioactive goo. After 90 minutes,…

A: topic- exponential function

Q: Suppose that the position of a particle is given by s(t) = 6t³ + 2t +9. (a) Find the velocity at…

A: See the details solution in below

Q: Identify the type of conic section whose equation is given. 2x2 = y2 + 2 parabola ellipse…

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Q: The area of the surface obtained by rotating the curve y = √√x + 1, for 0 ≤ x ≤ 2, about the x-axis,…

A: Given :

Q: Find the directional derivative of f(x, y) = 3x² - 2y² at point ,0) to point 3 (-2-1,0) 0(0,1). in…

A: Let's find directional derivative.

Q: Find the following limits (if they don't exist write DNE, ∞ or -∞ as appropriate): Answer: x-1 lim…

A: We need to find the limit limx→∞ x-12x2-7x

Q: Use the method of variation of parameters to determine the general solution of the given…

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Q: Exercise (c) Use the results of part (b) to estimate the slope of the tangent line to the graph of…

A: Given.

Q: A tank contains 40 gal brine for which the concentration is initially 3 lb/gal of salt. A brine…

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Q: y 42², x², y y = 0, x = 4

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Q: Use this to find the equation of the tangent line to the parabola y = 3x² - 2x + 7 at the point (-2,…

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Q: Sketch a right triangle corresponding to the trigonometric function of the acute angle 8. sin(8) =…

A: topic- trigonometric ratios

Q: The population of mosquitoes in a certain area increases at a rate proportional to the current…

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Q: A farmer wants to enclose a rectangular area with 400 feet of fence. In order to maximize the area…

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Q: Write an equation for the transformed logarithm shown below, that passes through (1,0) and (0,2) 5 4…

A: Please see the below picture for detailed solution.