SOLVE THE FOLLOWING PROBLEM AND SHOW YOUR COMPLETE SOLUTIONS. EXPLAIN YOUR WORK FOR BETTER UNDERSTANDING. 6. f 5x²+2x+5 dx 3 x +x-2

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

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A: We have to perform the partial fractions

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Q: 1 e e 5. If A-), then ¹-(3) = eª = 01 0 e

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Q: Find the volume of the solid generated when the shaded area is revolved about y = -1. y y = 2x y=x²…

A: To find the volume of the solid generated when the shaded area is revolved about .

Q: Find the domain of f(x). f(x) = Interval 3x - 5 x² + 2x - 35 Answer Attempt 1 out of 2 2 Answer…

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Q: Suppose we have a triangle with A 40°, B= 60° and c = 4. Then a =

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Q: A biologist has two brine solutions, one containing 2% salt and another containing 8% salt. How many…

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Q: Find the domain of f(x). f(x)=√x² + 9x - 8

A: Here we will find the domain of the given function on solving the quantity under root putting…

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Q: 1. Find the area between the two curves. Be sure to show the representative rectangle in the 1st…

A: Given functions are,y=f(x)= 8 cos x and y=g(x)= sec2x

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: A curve with polar equation r = 28 5 sin +41 cos 0 represents a line. This line has a Cartesian…

A: A curve with polar equation represents a line.To find the Cartesian equation of the line in the…

Q: d) Write an expression that represents the approximate value of g(x) for a generic value x in the…

A: The graph of the function g'(x) is shown as,

Q: Use trigonometric identities to solve the equation in the interval [0, 2). 2 cos ²0-sin 0-1=0

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Q: You have to examine the relationship between the age and price for used cars sold in the last year…

A: From the above table we…

Q: Use a Maclaurin series in this table to obtain the Maclaurin series for the given function. f(x) =…

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Q: Evaluate S 2x + 1 (4x + 3)(x + 1) - dx

A: Consider the integral

Q: Suppose f(1) = 2, ƒ'(1) = 3, ƒ (2) = 1, ƒ'(2) = 4, and g(1) = 3,g'(1) = 5,g(2) = 1,g′(2) = 4. If…

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Q: Find the area of the region between the curves y = x(1-x) and y = 4 from x=0 to x = 1.

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Q: 9. Let f(x) = sinx, g(x) = cos x. The functions f and g, considered on the interval 0, π], are…

A: Given that the function are

Q: 8. An engineer invests $27,000 in two bonds. If one 7% and the other yields 9%, how much is invested…

A: Let engineer invest $x on one bond which yields and  on another bond which yields

Q: 5. If f(5) = 7.8 and ƒ' (5) = 5.2, then use the linear approximation (also called the tangent line…

A: The linear approximation of a function f(x) at x=a is given by

Q: how that the function is increasing on the given open interval. (Enter your answers as a…

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Q: Let g(x) = f(t)dt, where f is the function whose graph is shown. y f 20 (a) Evaluate g(0), g(4),…

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Q: Given f is concave down and ƒ (4) = −2 and f1 (4) = 3. What is the estimate for = 4? Is it an…

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Q: Solve the rational inequality x²-9 x² - 49 -≤0.

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Q: Find all solutions of the equation in the interval [0,2+). 2 sin 20-3 sin 0+1=0

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Q: Consider the following function. T 3 π f(x)=sinx, a ==, n=4, 0≤x≤: 6 a) Approximate f(x) by a Taylor…

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Q: The position of a particle moving along a coordinate line is s=√52+4t, with s in meters and t in…

A: The position of a particle moving along a coordinate line is s=52+4t, with s in meters and t in…

Q: 5. Find the length of the curve • r(t) = cos(t)i + sin(t)j +ln(cos(t))k 0≤t≤n/4

A: since you have posted multiple question in this question which are not interlinked so i have solved…

Q: If f(x) - Sto = t5 dt then f'(x) = and ƒ'(−4) =

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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

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

A: Consider the curve

Q: 1. Find the area bounded by x = y²; x = −2y² +3

A: To find the area bounded by

Q: Find the area of the region between the curve and the x-axis. 2 f(x)= x(x² -26), from - 5 to 5.

A: The region is bounded by curve  and x-axis from

Q: Find the exact length of the curve described by the parametric equations. x = 8 + 3t², y = 7+ 2t³,…

A: x=8+3t2

Q: Evaluate the surface integral      SF · dS  for the given vector field F and the oriented surface…

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Q: At what value(s) of x on the curve y=-7+90x^3-3x^5 does the tangent line have the largest slope?

A: y=-7+90x3

Q: (b) Use Desmos to graph the surface area function on the following coordinate system. Label each…

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Q: Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an…

A: The objective of this question is to find the critical numbers of the given function f(x) = 12x -…

Q: is it 3and -2 for A?

A: y=x2-6x+7

Q: Find an antiderivative of the function g(t) = e-³t. An antiderivative is

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