Evaluate the following integral. 2 | (0²-0 -2 (4y -6y+6) dy

Q: Evaluate the following: lim In(e+h)-in e

A: To evaluate the following limit.

Q: Given the definitions of f(x) and g(x) below, find the value of g(ƒ(8)). f(x) = X 11 g(x) = x² + 7x…

A: The given functions  and .The aim is to find the value of .

Q: Express your answer as a polynomial in standard form. f(x) = -3x + 5 g(x) = x² + 2x + 15 Find:…

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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: 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. 2 f(x)= x(x² -26), from - 5 to 5.

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

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

A: The objective of this question is to find out the amount of each brine solution needed to create a…

Q: d. y = 2x+1 x²-4 5x+1 e. y = 2√x-1 f. y = sin x ln x-1 x²+1/

A: To find the derivative of the following functions.

Q: A tall pipe is 30 feet tall. A person with a height of 6 feet walks away from the pipe along a…

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Q: Find the parametric equation of a line segment with endpoints (1,4) and (5,-2). Find the parametric…

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Q: 1. Solve the system of equations 7₁-272 +373 2₁-22 +22 271-72 +373 b₁. b₂. ba

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Q: Two cylinders are given. The larger cylinder is a dilation of the smaller cylinder. Part A:…

A: Smaller length = 2mLarger length = 9mVolume of the smaller cylinder = 24 pi m3

Q: Find the mass of the solid bounded by the planes x + z = 1, x-z=-1, y = 0, and the surface y = √2.…

A: Given that the solid bounded by the planes  and the surface .The density of the solid is

Q: x+6 (x + 2)2 dx

A:

Q: If f(x) f'(x) = = x² S²³ to dt then

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Q: Sketch the graph of the piecewise-defined function. Write the domain and range of the function. |x,…

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Q: = sin(x),0 ≤ x ≤ π

A: Given that the expression

Q: Find the linearization L(x) of f(x) at x = a. f(x)=x+, a= 2 3 O A. L(x)=x+1 3 2 23 OB. L(x)= x+3 5…

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Q: Express the function as a power series by first using partial fractions. f(x)= 2x+5 x2+5x+4

A: Given: f(x)=2x+5x2+5x+4let's first factor the denominator and then use partial fractions.The…

Q: Refer to the graph shown below and evaluate Ĵ 1941 CH - 4 f(t)dt.

A: Consider the figure

Q: f(x) = -3x + 5 g(x) = x² = x² + 2x + 15

A: Given the function   we have to find the value of (gof)(x)

Q: 31. 3 1-25x2 dx

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

Q: Find the critical numbers and the open intervals on which the function is increasing or decreasing.…

A: The objective of this question is to find the critical numbers and the open intervals on which the…

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: Find the unit tangent vector T(t) at point P. r(t) = t²i + tj + 20 k, T(5)= X P(25, 5, 20/3) Find a…

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Q: . If an item has a new cost of C and an annual depreciation rate of r (as a decimal), its value, V,…

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Q: The point(s) is/are (Type an ordered pair. Use a comma to separate answers as neeeded.)

A: Given that the graph with tangent line parallel to y=3x+1 we have to find the point is/are?

Q: Given the definitions of f(x) and g(x) below, find the value of (fog)(2). f(x) g(x) = X = -x+ 2 2 _…

A: Given:

Q: Biologists stocked a lake with 300 fish and estimated the carrying capacity (the maximal population…

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Q: (4) Find the maximum and minimum values of f(x, y) = xy on the ellipse x² - xy + y² = 1.

A: The given equation of function  Let

Q: Find the integral. Use C for the constant of integration. | (x² (y² + 3)² dy

A: The objective of the question is to find the integral of the given function with respect to y. The…

Q: Find all exact solutions on the interval [0, 27). If there is more than one answer, enter them as a…

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Q: Find the logarithm. 1 log 5 625

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Q: 0 1 2x (4 – x²) dx

A:

Q: Highest point on the major axis: (2,11) Lowest point on the major axis: (2,-1) Rightmost point on…

A: The given equation of ellipse

Q: Find the absolute max. and min. of each function y=√4−x^2, (−2,1)

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

Q: Approximate the critical numbers of the function on the open interval shown in the graph. Determine…

A: The objective of the question is to identify the critical numbers of the function and determine the…

Q: Find the domain of the following function. f(x) = log 3 (x-4)

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Q: The equation of a hyperbola is 64 a) Find the center, vertices, transverse axis, and asymptotes of…

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Q: The function f(x)=x² +1, x ≥0 is one-to-one. (a) Find the inverse off and check the answer. (b) Find…

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Q: Evaluate the integral by making an appropriate change of variables. JJ₂² 7 cos(3 (y + x)) dA where R…

A: The given integral  where R is the trapezoidal region with vertices

Q: f(x) = x² Which of the following is the linear approximation of f(x) at the point a=16? O O O 3…

A: f(x)=x3/8, a=16

Q: What is the domain of the function shown in the graph below? -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 10 9 8 7…

A: To find the domain of the function shown in the graph below.

Q: Stoite the Fundamental Theorem of Calculus?

A: we need to write down the fundamental theorem of calculus.

Q: Determine the following indefinite integral. 5-6 sin¹ (2) cos(x) dx

A:

Q: Find the position and velocity of an object moving along a straight line with the given…

A: The integration of acceleration function gives velocity

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: 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: Given the graph of f(x) below. Determine the average rate of change of f(x) from x = -2 to x = 2.…

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Q: Express your answer as a polynomial in standard form. f(x) = 2x² 5x – 12 - g(x) -2x + 2 = Find:…

A: f(x)=2x2-5x-12g(x)=-2x+2