Determine lim f(x) given the definition of f(x) below. (If the limit does not exist, enter DNE.) [-2x² + 3x - 1 -1 -2x² + x f(x)= if xs-4 if -4

Q: Find the radius of convergence and the interval of convergence of the power series. M8 n=1…

A: Radius of convergence is half the size of interval of convergence.And we use ratio test to find the…

Q: Find the area of the region between the curve and the x-axis. f(x) = 16-x², from - 7 to 7

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Q: 1. A rock is thrown upward with a velocity of 20 meters per second. Its height, in meters, t seconds…

A: According to our guidelines, we can answer only first question (due to multiple questions). Kindly…

Q: 5. Using Geogebra, draw the polar curve, r = sin³ (2.50) +cos³(2.50),0 ≤ 0 ≤ 2ñ.

A: Consider the curve

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Q: A 17 ft. ladder is leaning against a building. The foot of the ladder is currently 9 ft. from the…

A: We have to use the concept of derivatives

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Q: Given y = f(u) and u = g(x), find - (3) ² y=9u-5, u= dy dx = f'(g(x))g'(x).

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Q: The answer is wrong

A: The given curves equation is

Q: Jasper Furnishings has $200 million in sales. The company expects that its sales will increase 13%…

A: The simple linear regression provides us with a mathematical relationship between two variables on…

Q: 37. se sec² (10x + 7) dx

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: 2. For the function g whose graph is shown, state the following. (b) lim g(x)= x-0 (a) lim g(x)=…

A: The graph of the function is given.The aim is to find the e)The equation of the vertical asymptotes.

Q: Consider the following function. g(x) = (x - 2)²-9 Step 3 of 4: Find two points on the graph of the…

A: Consider the function

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A: The rate of change is equal to derivative of function given.So at first we would differentiate S(t),…

Q: Use the Ratio Test to determine the convergence of the following series. 8 Σ(-1)n+1 n=1 5 nn n!

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Q: Find an equation of the line tangent to the curve at the point corresponding to the given value of…

A: Given,

Q: Convert the Cartesian coordinate (1,-2) to polar coordinates, 0 ≤ 0 0 r = Enter exact value. 0 =

A: Cartesian coordinate (1,-2)

Q: 2. f(x) = = 1 1+72) [0,4], n = 4 , 1+x²¹

A: The given curve .The aim is to find the area under the curve using right-hand approximation in the…

Q: Set up, but do not evaluate, an integral for the area of the surface obtained by rotating the curve…

A: y = xe-x , 1 ≤ x ≤ 7

Q: f(x)=x^[8/3]-4x^[2/3] determin the: a) roots b) Domain c) intervals for which the function is…

A: The given function is To find:-rootsdomian intervals for which the function is positive and negative…

Q: Find the exact location of all the relative and absolute extrema of the function. (Order your…

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Q: At time t=0, a particle is located at the point (1,5,4). It travels in a straight line to the point…

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Q: The input value x = a is in the domain of the function g'. Explain the meaning of g'(a). Write an…

A: “Since you have posted a question with multiple sub parts, we will provide the solution only to the…

Q: Find y'' if y=-6 cos x. OA. y' = 6 sin x OB. y' = 6 cos x OC. y'= -6 cos x OD. y'= -6 sin x

A: The function is given byTo determine: The expression of the second derivative of the function.Formul…

Q: (– ²/6) has exactly one point of inflection with a positive x-coordinate. What is the x-coordinate…

A: The given function is .The aim is to find the point of inflection.Definition:If  is an inflection…

Q: Find all exact solutions on the interval 0 < 0 < 360°. If there is more than one answer, enter them…

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Q: Given the graph of the function f (a) below, use a left Riemann sum with 4 rectangles to approximate…

A: Given the graph of the function  below, by using  a left Riemann sum with 4 rectangles to…

Q: Consider the triangle below. Click on the picture to see it more clearly. If c = 4, the angle C =…

A: Given,

Q: (a) Estimate the area under the graph of f(x) = 1/x from x = 1 to x = 2 using four approximating…

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Q: Convert the rectangular coordinates of the point to polar coordinates (r,0) with r>0 and 0 ≤0<2.…

A: We need to convert rectangular corrdinates to polar coordinates.

Q: Find a power series representation for the function. ( ) = n( 11 + y )

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Q: 1. Decide whether each of the following sentences is valid, satisfiable or unsatisfiable: a) Smoke…

A: Here given a different sentences.The objective is to check that the given sentences are valid,…

Q: Find the volume of the solid obtained by rotating the region = bounded by the x-axis, the y-axis,…

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Q: Evaluate the iterated integral. LT (3) (3x - 2y) dy dx

A: we need to evaluate the given double integration.

Q: e area of the blue region. It is the area under the curve. y 10 8 6 4 2 y = 3x+1 y = 6-x X 1 2 3 4 5…

A: The graph of the function is given.The aim is to find the area of the blue region.

Q: Use the test-point method to solve the polynomial inequality. x³ - 6x² ≥0

A: By using the test-point method to solve the following polynomial inequality.

Q: Express equation in the form y = f(x) (eliminate the parameter). a. c(t) = (t-¹,t-²) b. c(t) = (et,…

A: There are three different questions given. As per our company guidelines, we are supposed to solve…

Q: Determine if the following function is continuous and differentiable at x = 0. ex - sin x f(x) = {…

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Q: Find an antiderivative F(x) with F'(x) = f(x) = 6e² and F(0) = 4.

A: F′(x)=f(x)=6e2x and F(0)=4

Q: Functions f and g are given as follows. X 5 X+2 x + 2 Find each of the following functions and state…

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Q: ∞ 4. Apply the Ratio Test to the series [ the limit lim n→∞ (3n)! n=12¹ (n!)3 an+1 an and find

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Q: A small resort is situated on an island that lies exactly 6 miles from P, the nearest point to the…

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Q: Find the points on the graph of the polar equation where the tangent line is horizontal or vertical.…

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Q: Determine whether the series is absolutely convergent, conditionally convergent, or divergent. M8 Σ…

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Q: When solving the auxiliary equation associated with the differential equation 3y"+2y"=0 it is…

A: .

Q: SOLVE THE FOLLOWING PROBLEM AND SHOW YOUR COMPLETE SOLUTIONS. EXPLAIN YOUR WORK FOR BETTER…

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Q: 9. Find the interval of convergence of the series: 2¹ (x + 3)¹ In(n) ∞ n=2

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Q: lim n→∞ (1 + 1/2 ) ² = 2n

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Q: 4. Using Geogebra, draw the parametric curve, x = sin³t+cos³t; y = sin² t - cos²t,0 ≤t≤ 2n-

A: The given curve is,The given interval is,

Q: 5. Find two antiderivatives of f(x) = x0.8 - 3e²¹ + π cos(2x)

A: