Use the comparison theorem with f(x) = = 1 √x to show that [₂²= 1 √x-1 is divergent.

Q: Graph the function. Plot all necessary asymptotes. Plot at least 4 points. For vertical asymptotes,…

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Q: If f (x) = x² - x and g(x)=√x-2, what is (fog)(x) ? Simplify your answer. x²-x-2 /x² - 2 2-x-2 O…

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Q: Use the Monotone Convergence Theorem to show that the sequence n! +∞o (1 · 3 · 5 ··· (2n − 1)) n = 1…

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Q: Solve the initial-value problem. +3dy + 3t²y = 8 cos(t), y(t) = 0 dt

A: We have to solve this initial value problem.

Q: A function is given. g(x) = 7 + 1/2x;    x = 1, x = 7   (a) Determine the net change between the…

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Q: Find the equation of the tangent line 7 to the graph of f at the given point. Use this linear…

A: The solution is given below

Q: Suppose f is a differentiable function of x and y, and g(r, s) = f(2rs, s² - 6r). Use the table of…

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Q: If cos(0) = sin(0) = - 1 and is in quadrant III, find the exact value of sin(0). 9

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Q: Σ + 1 + sin2 η 10η n=1

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Q: Use the gradient to find the directional derivative of the function at P in the direction of Q. f(x,…

A: We know that the directional derivative of a function f(x, y) at a point P in the direction of a…

Q: 3. Using multiple linear regression, estimate the values of a, b and c in the given regression…

A: given that        X            1            2              3            4          Y…

Q: 1 10. Sketch the graph of g(x)= - - cos7x, using the amplitude and the period. 7

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Q: N Given the series an, let SN=an be its Nth partial sum. Suppose that n=1 n=1 SN=8- A) Find a3. 5 N²…

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Q: f(x) Suppose that f(x) and g(x) are differentiable functions such that f(7) = 2, f'(7) = 6, g(7) =…

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Q: Find the differential dy of the given function. y = √3-x² dy X 3 - x Submit Answer =dx 2

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Q: f(t) = 3 Sgh(st) - ans: F(W) = 2013 1+jt гпе

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Q: What value(s) of 8 are an appropriate choice when proving the following limit? lim (10x + 4) = 44…

A: We have to solve the above problem of limit.

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

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Q: If f(x)=√10- x and g(x) 3x² 10 - 3 x²√10 x - O 3√10-x x² X Ox²√10-2 3 O None of these. 3 g(x) find…

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Q: If f(x) = 3x²-3x + 2, find f'(1). Use this to find the equation of the tangent line to the parabola…

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Q: Find the minimum and maximum values of the function on the given interval by comparing values at the…

A: Given  y = x3-24 lnx+7,  12, 3.

Q: What value(s) of 8 are an appropriate choice when proving the following limit? lim (√6x +30) = 0…

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Q: For the graph below, identify a restricted domain for which the function has an inverse that is also…

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Q: The total stopping distance T of a vehicle is shown below, where T is in feet and x is the speed in…

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Q: Find the volume of the solid that results when the region enclosed by y = √√√x, y = 0, and x - NOTE:…

A: Understanding of volume of solid after revolution is required to solve these problem.

Q: Find a polar equation for the curve represented by the given Cartesian equation. (Assume 0 ≤ 0 <…

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Q: Suppose you need to know an equation of the tangent plane to a surface S at the point P(3, 1, 3).…

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Q: A circular plate with radius 9 m is submerged vertically in water as shown. Express the hydrostatic…

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Q: function is given. g(x) = 7 + 1/2x;    x = 1, x = 7   (a) Determine the net change between the…

A: Topic:- calculus

Q: A vendor at a carnival sells cotton candy and caramel apples for $2 each. The vendor is charged $175…

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Q: (c) f(x) > 0 The solution set is (-2, 0) U (4, 00) (d) f(x) ≥ 0 The solution set is 10.01 (0,0)…

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Q: 9. Estimate the value of the convergent series 8 k=1 (-1)^² k! + 2k with an absolute error less than…

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Q: Let f(x) = 3x + 2. Determine (fofof)(x). (fofof)(x) =

A: The given function is: fx=3x+2   As we know that; f o f o fx=fffx

Q: K If f(x) = x² + 7x and g(x) Answer = 51 find g(f(n)). g(f(n)) IL

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Q: 6. Find y" give y = 7³x a) 21³x In(7) b) 63³x In(3) c) 3(7³x)ln(3) d) 9(7³x)(ln7)

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Q: Write an expression for the nth term of the sequence. (Your formula should work for n = 1, 2, ....)…

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Q: What is the average rate of change of f(x) from x₁ = 3.8 to 2 = 7.2? Please write your answe rounded…

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Q: We are trying to prove the following limit. Suppose that we have found a value of such that e =…

A: Given: limx→7 (2x-7)=7

Q: 7. Two part question: a. Determine the equation for the slope of the secant line between the point…

A: The given problem is solved below in detail.

Q: Determine whether the following series converges or diverges: 2. 1. +00 Σ n=1 1 + sin2n] 10n +00 ΣΕ…

A: We need to determine whether the given series converges or diverges

Q: ГО Г0 1 3 2 -а 1 2 123 b 1 3 1 0 1 0 0 3. C Ld. 324 [5]

A: 0132212313101003abcd = 3245 from this find a,b,c,d using gauss elimination method using this method…

Q: In the IS-LM framework, the OA policy, borrowing OB. bank; prime OC. borrowing, policy OD. lending;…

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Q: Evaluate the integral: 3 X sin ³ COS 3 3 X col 3

A: Solved below.

Q: Evaluate the limit: lim h→0 (−5+h)² - 25 h

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Q: The graph of y=f(x) is given. Solve the inequalities. Write the solution sets in interval notation…

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Q: Complete the equation for the piecewise function graphed below. +6+ 5 -4- 3- 2 + -6 -5 -43 -2 -1 H…

A: For any straight line ,we need know two points, Here from -6≤x≤2 clearly line passing through two…

Q: Determine whether the series below converges or diverges. If the series converges, find its sum.…

A: Expand the given summation

Q: Question 11 For the function f(x): a. the x and y intercept b. the vertical and horizontal…

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Q: Find the general solution of the differential equation. y(5) — 11y(4) + 29y"″ − 11y" + 28y' = 0.…

A: Let's solve given diffrential equation.

Q: Consider the following table of values of the functions f and g and their derivatives at various…

A: Aim: Dxf(g(2)) We know that,…