sin 5x dx

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Q: Should like radicals remind me of like terms?

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Q: Find the indefinite integral ∫x+1√xdx.

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Q: Example: Simplify: (1+ i)" + (1– i)".

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Q: Explain why each of the following integrals is improper  integral -infinity to infinity  x2 e -x2 dx

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Q: (a) Find an approximation to the integral  ∫04      (x2 -3x) dxusing a Riemann sum with right endpoi...

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Q: Find the indefinite integral ∫ sin x/(1 + cos x)   dx

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Q: Solve a, b, and c show all work

A: To find in terms of y.

Q: Check the validity of Cauchy’s mean value theorem for the functions f(x)=x4 and g(x)=x2 on the inter...

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Q: ,determine the partial fraction decomposition of the given rational function. Q.3x +4/x2(x2+4)

A: Given,   

Q: the sequence. an aq = 6, an+1 = 1+an

A:  

Q: Let f(x) = x2 + 1 and g(x) = 2x – 3. Find the following. %3D f(g(4)) g(f(4))

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Q: Write number in scientific notation. 32,000

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Q: Write and evaluate the definite integral that represents the area of the surface generated by revolv...

A: Given that, y = √(25 − x2) , −4 ≤ x ≤ 4 Formula: If the nonnegative function f(x) is continuously di...

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Q: Find any intercepts y = 2x − √(x2 + 1)

A: x-intercepts are the points at which the graph of given curve meets x-axis. That is, the points at w...

Q: Find the global maximum and global minimum of the function f(x)=x2−16x on the interval [−4,−1].

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Q: The variable s is proportional to t, and s = 25 when t = 75. Determine t when s = 60.

A: Now given that, s = 25 when t = 75. Therefore we get,

Q: Use a graphing device to graph the following polar curves. Sketch the graph and explain how you dete...

A: (a) Consider the given polar equation r = esin(θ) - 2cos(4θ) The period of sin and cos function is 2...

Q: Find the volumes of the solids The solid lies between planes perpendicular to the x-axis at x = π/4 ...

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Q: Find the power series for the function using the suggested method. Use the basic list of power serie...

A: Given Data The function is f(x)=( ex+e-x) /2.   The power series of ex is, The power series of e-x ...

Q: Find a possible equation for the polynomial whose graph is given

A: The x-intercepts of the graph are x=-2,x=-1,x=1,x=3 Therefore, the factors of the polynomial are x+2...

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A: Let x GB of data will cost the two data plans same. Now given that, Data Plan A has a monthly fee of...

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Q: Use the graph shown in the figure. Identify or sketch each of the quantities on the figure. (a) f(1)...

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Q: Find the power series for the function using the suggested method. Use the basic list of power serie...

A: Given that, f(x) = ex^2 The power series expansion for ey is,  

Q: A tank is full of water. Find the work W required to pump the water out of the spout. Use the fact t...

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Q: Calculate the derivative of the function y=arccos x arctan x at x=0.

A: Differentiating with respect to x, we get

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A: Given differential equation is Integrating both sides, we get

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Q: Evaluate the integral ∬Rxydydx, where the region of integration R lies in the sector 0≤θ≤π2 between ...

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Q: Find the natural domain and graph the functions

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Q: Prove that for any positive numbers a and b the inequality ab+ba≥2 is valid.

A: It is required to prove for any positive numbers a and b.

Q: Gradient fields in ℝ3 Find the vector field F = ∇φ for thefollowing potential functions.

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Q: 39. Find two numbers a and b with a < b such that [(6 - x - x) dx has its largest value.

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Q: A ski jumper travels down a slope of the height H and leaves the ski track moving in the horizontal ...

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Q: find the center of mass of a thin plate of constantdensity d covering the given region. The region b...

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Q: Calculus Question

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Q: Suppose that the Celsius temperature at the point (x, y, z) on the sphere x2 + y2 + z2 = 1 is T = 40...

A: We have given; The temperature T at any point (x, y, z) in space isT = 400xyz2and the unit spherex2 ...

Q: Find a potential function for F or determine that F is not conservative. F = (cos(z), 16y, -x sin(z)...

A: The vector field given in the question is: F = &lt;cos(z), 16y, -xsin(z)&gt; Hence, F1 = cos(z), F2 ...

Q: Find the Taylor polynomials (centered at zero) of degrees 1, 2, 3, and 4. f(x) = e¬X/3 (a) degree 1 ...

A: Given:

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Q: Find a polar equation for the curve represented by z +² = 8cz, where e is a constant.

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Q: Solve the differential equation dy /dx = x sq / y  sq (b) Find the solution of this equation that sa...

A: By separating the variables, we get

Q: In Exercises 65–70, find the limit of f as (x, y)→ (0, 0) or show that the limit does not exist. x* ...

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Q: (a) The curve y=  |x| /√ (2 -x2)is called a bullet-nosecurve. Find an equation of the tangent line t...

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Q: Please answer it clearly and elaboratly without skipping any steps

A: Since you have posted multiple question, we will solve first question for you. To get remaining ques...

Q: Solve B show all work

A:

Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.