A. Evaluate the following integrals: | cos 4x cos 2xdx 3.

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Q: The exact differential d(xy)= xdy+ ydx , what is the d O= 4x²y°dy+ 2xy*dx.

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Q: hort proof. 5. Show that cot 0 d0 is equal to In|sin 0| + C.

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A: Since, given that cot θ=-5And we know that cot θ=BasePerpendicular=-51Since, by pythagoras theorem, ...

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Q: S 2xln(1+ x)dx

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A: Given f is differentiable on (a,b). and c lies in (a,b) such that f'(c)=0.

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A: We will find the rate of change of hypotenuse. 

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Q: b) y = (-x – 1)2 + 2 3 1 -5 -4 -3 -2 -1 1 2 -1 -2 -3 -4 Vertex: Left: Right: 4) 4, 2.

A: The given function,     y=-x-12+2

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A: We have to find value of f(x)

Q: 5. Sand is pouring from a hole at the rate of 25 cubic feet per second and is forming a conical pile...

A: Solution ) dv/dt = 25 ft3/ sec  h = d/4  d = 4h  [ d = r/2 ] r/2 = 4h  r = 2 × 4h  r = 8h  h = 5 fee...

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Q: ƏM 3. In the differential equation (y -x -4x–1dy+2y(x+ y+ 2)dx =0, 4. In the differential equation (...

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Q: If the integral from 0 to 2 of the function g(x) is equal to 3, what is the integral from 0 to 2 of ...

A: Since you have asked multiple questions in a single request we would be answering only the first que...

Q: 8. lim xcot3x

A: Given; limx→0xcot3x So, We can also write as; limx→0xcot3x=limx→0x1cot3x=limx→0xtan3x   ...We know: ...

Q: need some assistance with problem #16, please?

A: Topic:- application of calculus

Q: Verify that the points are the vertices of a parallelogram, and find its area. A(1, 1, 3), B(8, -2, ...

A: FIND THE AREA

Q: Find the indicated partial derivatives of: -8x 7y - f(x, y) 5а + 2у fr (x, y) = fy(x, y) =

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Q: sec? 5x dx

A: Given query is to find the integral .

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Q: Vrite an integral that is equivalent to æf (x²) dx. a = b = f(u) du submit Answer

A: Given query is to write equivalent integral.

Q: Find two vectors in opposite directions that are orthogonal to the vector u. (The answers are not un...

A: The given vector is u=5,-4,8. Let the orthogonal vector to u be v=a,b,c. Since they are orthogonal S...

Q: Sketch the curve x^2+ x^2y^2 = a^2y^2, a > 0. Enumerate the steps in your solution

A: Given curve, x²+x²y²=a²y²....a>0 So, x²(1+y²)=a²y²

Q: Evaluate the integral

A: answer of given question is in next step

Q: given the curve: y = 4cos3x - 3cosx, find the following values of x (from 0 to 2pi radians) when y ...

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Q: Determine D103 (cos 2x).

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Q: Find the component form of u + v given the lengths of u and v and the angles that u and v make with ...

A: Solution: we know that u→=ucosθ i +usinθ j

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Q: Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval? f(x) = ln...

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Q: Match the second-degree equation to its graph. A. C. r² + y? + 2? – 2x + 2y + 4z + 6 = 0 r² + y² + z...

A: A The equation is x2+y2+z2-2x+2y+4z+6=0  x2+y2+z2-2x+2y+4z+6=0x2-2x+y2+2y+z2+4z=-6x2-2x+1+y2+2y+1+z2...

Q: Obtain the particular solution satisfying the initial conditions indicated. 1. e* (3x°y-x)dx+e" dy =...

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question fo...

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Q: 1. Find the volume of the solid formed by revolving the region bounded by the graph of f (x) = -x² +...

A: Given problem:- Find the volume of the solid formed by revolving the region bounded by the graph of ...

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Q: Consider the following function and closed interval. f(x) = x3 - 4x2 – 16x + 5, [-4, 4] Is f continu...

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Q: Given the piecewise function defined below, determine the value of 3 f(x)dx in simplest form. -3x² –...

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Q: 1. Integrating factors found by inspection: (xy + xy)dx+(x²y²-2)dy = 0

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A: To determine whether the lines intersect, and if so, to find the point of intersectionx3=y-2-1=z+1, ...

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Q: iven vector u = (-1, –5) and v = (-2, –1) , determine the value of 5v – u in omponent form.

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