The function f(x), which is defined for a ≤ x ≤ b, has the following behavior: f'(x) < 0 and f" (x) > 0. Choose the graph that best represents y = f(x)

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A: We need to do integration of  sin2(2x)  First we will apply it's formula, since this value is equal…

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A: Here, the area bounded by the curves: y=x3+1 and x-axis  with the limits x=0 and x=3 is:

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A: We sketch the given region using a graphing calculator as shown below:   The shaded region is…

Q: fsec³ 7x tan5 7x dx 4.

A: Let's solve given integration.

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Q: 9 To express Q(x) = cos(4x-5) as the composition of three functions, identify f, g, and h so that…

A: The given function is  Q(x)=cos9(4x-5).

Q: (6) Sketch a graph of a function, f, that has the following properties: • lim f(x) = 3 and lim f(x)…

A: Given information:  ----------------------------------------------------------------------------…

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Q: The following differential equation is a Bernoulli equation: 2 dy + = y³ y3 where y = f(t) dt t By…

A: The following differential equation is a Bernoulli equation:dydt+yt=y23 where y=ftBy making the…

Q: Solve the following matrix equation for a, b, c, and d. a-b b + c |-|8 8 3 88 3d+c 2a - 4d a = b =…

A: We will find the value of a ,b ,c ,d by solving the given matrix equation in the following step.

Q: (Requires a short but nontrivial geometric Let ABC be a triangle argument.). with angles…

A: Using sine rule, length of other two side are evaluated.

Q: I. Evaluate the following limits. 2. lim (x - Inx)* +0+x

A: We have to find the limit of the function  limx→0+x-lnxx. We can write,    u= elnu Therefore,…

Q: Perform the integration. 3 (13 (|3* − 1| + |3* − 3|) dx 0

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Q: II. Find the value(s) of x (or the interval of convergence) 2. Σn=0 for each of the following power…

A: The power series is  ∑n=0∞ (-1)n+1(x-5)nn·5n

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Q: What is the y = x^3 and y = x^2? O2/5 3/5 6/35 12/35 y-coordinate of the centroid of the plane…

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Q: 1. Use Comparison Test to determine the converges or diverges of the series Σ: 8 n=1 (n+1)√n

A: By using Comparison Test to determine the convergence or divergence of the series ∑n=1∞ 1n+1n.

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Q: Let f(x) = e2sinx 1. Find the absolute extremum values off on the interval [7]

A: To find the extreme values of given function at given  interval.

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Q: The integral of 3^4x dx is equal to * O 4^4x / In3 + C O 3^4x/In12 + C O 3^4x / In27 + C O 3^4x /…

A: SOLUTION-

Q: II. Evaluate the following integrals. 3. 12-2² | dr

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Q: 6. Find the area bounded by y= In x, y = 0 and x = e.

A: Area of a curve y=f(x) bounded by x=a, x=b is given by, A=∫abf(x)dx ln(e)=1, ln(1)=0

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Q: If F(x) a. F'(1) L √4t - t² dt, evaluate the following: x² b. F(2), by interpreting F(2) as an area

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Q: Using Laplace transforms, solve the initial value problem y" − 2y' + 10y = 0, y(0) = -3, y'(0) = 3.…

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Q: (³² sin æcosx tan³ xcot³ x sec xcscx dx

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Q: 3. Find the area bounded by a parabola and any right chord (use the parabola y2 = 4ax, chord x = x₁)…

A: In this question, we want to find the area bounded by the parabola and a right chord.

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Q: Find the area bounded by the curve y = coshx and the x- axis from x = 0 to x = 1. a. 11.75 sq. units…

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Q: The following differential equation is a Bernoulli equation: 2 dy = y³ where y = f(t) dt t By making…

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Q: 2. (9y-2 +6y-4-y-5+1) dy 3. √ (12x²-x²+x²) dx

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Q: Evaluate the integral of 3dx/(2x^2 + 4) from 0 to 0.2 *

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