Consider the following. [² x (x² - 1)³ dx 0

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A: calculate , how long it takes to for the amount in the account to double by using the compounded…

Q: Find the slope of the line tangent to the polar curve at the given point. (-5,75) 2'6 r = 5 sin 0;…

A: Slope of the line tangent to the polar curve is given by-

Q: Use the rules of differentiation to find the derivative of the function. f(t) = -5t² + 3t - 9

A: The function is f(t)=−5t2+3t−9The aim is to find the derivative of the function using the rules

Q: Use the given graph of the function g to find the following limits: 1. lim g(x) = help (limits) 22-…

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Q: You are given the differential equation satisfying y (+) = -2. The solution can be written in the…

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Q: 2. This question concerns the graph of the function x² (2x²-8) x(2x - 5)√4x²+3 y = f(x) = = (a) What…

A: The given functions  is

Q: Make a sketch of the region and its bounding curves. Find the area of the region. The region inside…

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Q: In how many different ways can 5 identical green shirts and 5 identical red shirts be distributed…

A: 5 identical green shirts and 5 identical red shirts be distributed among 6 children such that each…

Q: Let h(x) = x² + 2x − 6 - Determine the equation of the tangent line to h at x = 7. Report the…

A: We have given a function -6Put 7Point : Differentiating equation with respect to xPut Slope(m)=

Q: Suppose v₁ and v₂ are vectors with |v₁|= 2, |v₂| = 3, and v₁ v₂ = 5. Let

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Q: Consider the graph of a function f shown here: 3 (c) 6 ƒ(9) — ƒ(6) 9-6 (d) f'(3) ? 9 Using the…

A: From the given graph

Q: 9. The position of Minnie the mouse, as she moves back and forth along a horizontal line is given by…

A: Given that  position of Minnie the mouse given by equation is

Q: f(x, y) = x² + y² as (x, y) → (0, 0). Assume that polynomials, exponentials, logarithmic, and…

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Q: 84. x = e¹ sin t, y = e' cos t; 0 ≤ t ≤ 2π

A: As we know The arc length of the parametric curve (x(t), y(t)) over the interval [a,b] is

Q: ●find the derivative of the following by first expanding or Simplifying the expression g(a) = x ²-1…

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Q: 4. For the graph of the function g below, (a) Does g(4) exist? (b) Does lim g(x) exist? x→4 -2 (c)…

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Q: 18. Find the average X-coordinate of a point in the region to the left of the parabola x = 1 - y²…

A: Given :- The parabola .To find :- The average x-coordinate of a point in the region to the left of…

Q: Question 2.12) Is there some value of k for which the following function is continuous at x =-1? +k²…

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Q: 4. For the graph of the function g below, (a) Does g(4) exist? (b) Does lim g(x) exist? x-4 (c) Is g…

A: Question no. 4(e):Given:To Find: To determine whether exist.

Q: Suppose that a volcano is erupting and readings of the rate r(t) at which solid materials are spewed…

A: There are some given values of r(t), We have to calculate the lower estimate, upper estimate, and…

Q: f(x) = √√√x + 2; a = 7

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Q: Find an equation or inequality that describes the following ob A sphere with center (1,4,1) and…

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Q: (c) 5.⁰ re3d. (d) L₁ 1000e* dx

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Q: Find an equation of the tangent plane to the given surface at the specified point. z = 4x² + y² -…

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Q: 15. The graph below shows the height, H (in cm), of a tomato plant 1 days after it is planted…

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Q: Given f(x, y) = 6x5 cos(y¹), find fxy (x, y) = fyy(x, y) =

A: given

Q: Suppose a > 0 and a 1. For the following statements, choose all that are true. loga (M - N) = loga M…

A: Here given a>0 and,For the given statement we have to find as per the properties of logarithm…

Q: (a) lim x→3 a2 _ 5+6 x² - 9 tan(x) x→/3 cos(x) (b) lim (c) lim (e4-3x) 818

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Q: 15. (1.3.36) Find fogoh, where f(x) = |x4| g(x) = 2x h(x) = √(x)

A: To find , where

Q: Use a tangent plane at (8,3) to approximate the value of the following function at the point (8.1,…

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Q: Estimate the intervals on which the derivative is positive and the intervals on which the derivative…

A: The derivative is positive (where the graph is going upwards) on the intervals and  the derivative…

Q: Find all zeros, noting multiplicities and behavior at the zeros, of the following functions:

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Q: Choose the correct graph for A and B

A: We have to choose the correct graph.From the conditions of Reimann sum we know that-If f is…

Q: Critical Thinking Question: to be agreed upon by the group, and written below by the recorder.…

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Q: or #18 - #20 - Find & in terms of using the formal limit & efinition. lim x1 = 0 x→1

A: Note:-Since you asked multiple questions , according to our policy we can asolve only first question…

Q: can you solve b ,c and d

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Q: Solve the LP problem, If no optimal solution exists, indicate whether the feasible region is empty…

A: To solve the following LP problem..Maximize  subject to

Q: Question 2.31) Show that the equation *¹²= 2x must have at least one solution on the interval (0,2).…

A: Question no. (2.31):To show that the equation  must have at least one solution on the interval .To…

Q: Textit) Find a formula for the parabola whose graph is given below: f(x) = (-2, 8) 4 (3, 8) (click…

A: To find the formula for parabola?Note- As per company guidelines for multiple questions posted we…

Q: A population of N individuals grows over time, t years, according to the equation: AN N = (2+ e ²¹)…

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Q: 8. (1.1.74) If f and g are both even functions, is the product fg even? If f and g are both odd…

A: if f(-x)=f(x) then f is called even function.If f(-x)=-f(x) then f is called odd function.

Q: Use the given graphs of the function f (left, in blue) and g (right, in red) to find the following…

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Q: 3x+2 Find the points on the graph of the function y = 2-3 where the tangent line is perpendicular to…

A: Slope of two perpendicular lines The given line is perpendicular to the tangent of the…

Q: Suppose that y = f(x) is a differentiable function for which the following information is known:…

A: Since you have posted multiple subparts question in this question and as per company guidelines i…

Q: Matching: Write the letter for the correct equation under its graph. Not all letters will be used.…

A: Transformation function h=Horizontal shift k=vertical shifta=scaling factor

Q: 12 If f(t) = find f'(t). f'(t) =

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Q: Consider the differential equation y"-10y'+25y = 0. The characteristic equation is The solution(s)…

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Q: Find the differential of the function f(x, y) = 5x² – 5xy + 6y² at the point (5,8) using Ax = -0.3…

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Q: Use the theorem of Pappus to find the volume of a torus (pictured here). Assume that a disk of…

A: Given:Disk of radius => a = 5x= b = 4To determine: The volume of torus.

Q: 39. A boatman wants to cross a canal that is 3 km wide and wants to land at a point 2 km upstream…

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