Evaluate the definite integral. dx

Q: Sketch the region bounded by the given curves, then find its area. y = 2x - x^2, y = 2x^2 - 4x

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Q: Give an example of a series Σn a_n that diverges but lim n->∞ a_n = 0

A: P-series Test : Consider the series           ∑n=1∞1np = 11p+12p+...(i) Series will converges if p&g...

Q: 3. If f(r, y) = x*y - 2x-4y, then the total derivative of f

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Q: Find an equation for the plane through points P(1, -1,2), Q(2,1,3) and R(-1,2,–1).

A: This question can be solved by applying the formula of equation of plane passing through three non c...

Q: Find the area of the triangle with vertices P(1, 5, –3), Q(0,0, 0) and R(2, 4, 1). NOTE: Enter the e...

A: use the cross product and determinant  for solving the area.

Q: x dxdy Evaluate the following double integrals by converting to polar coordinates.

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Q: (2+3i '8+i Evaluate the expression Express the answer 1+2i) rectangular form.

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Q: Parametrize the line that passes through the point (1,2,3) parallel to the vector v = -3i + 7k.

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Q: 5. x = 8 – y², x = y² – 8

A: This question is based on application of definite integral.

Q: We want to fit v = k1 * exp(-k2 * u) to the data: (0, 1.95), (1, 1.28), (2, 0.70) by least-squares f...

A: Solution

Q: 4. у%3D 2х—х2, y = 2x² – 4x

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Q: State both forms of the Chain Rule for calculating the derivative of y = f(g(x)). State both forms o...

A: We can answer both the questions as below

Q: Compute for the dot product between the following pairs of vectors. Also, using the dot product alon...

A: We can find the dot product and other required answers as below.

Q: +o0 Consider the power series (* – 1)" log n n=2 (a) Show that the resulting series when x = 0 is co...

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Q: the following statement true? If it is true, explain why it is true. If it is false, give an example...

A: Is the following statement true? If it is true, explain why it is true. If it is false, give an exam...

Q: The function y = 2x2 for -3 ≤ x ≤ 3 is given. a) Plot the graph b) Find the gradient at x = 1

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Q: 1) Parameterize the line segment running from (1, 2) to (3, 5).

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Q: 2n + 1 n -1 n tan n=1

A: Find the limit of the given equation at infinity.

Q: Find the derivative of the function at Po in the direction of u. f(x, y, z) = In(x 2 + 3y 2 + 9z 2),...

A: Since you have posted multiple questions i can do first question as per our company guidelines pleas...

Q: 1. Eliminate the parameter to find a Cartesian equation of the curve with parametric equations z = e...

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Q: Let A and M be n x n matrices. If AM = 31, then M-1 O is equal to (1/3) A is equal to (1/2) A O is e...

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Q: у%3D 2х — х", у%3D 2х — 4х -

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Q: Exercises: Sketch the region bounded by the given curves, then find its area. 1. y = x², x2, 2. x = ...

A: Area of the Region between the curves : If f(x) and g(x) be two continuous function on a,b and f(x)≥...

Q: 6) Find a) given: y=-+ (3x' +27) (use product rule) 2x² +5 given : y = b) (use quotient rule) 3x-4

A: Since you have posted multiple questions i can do first question (with both subparts)as per our comp...

Q: Find the area of the parallelogram that has u =i – 2j + k and v = 3j +k as adjacent sides. NOTE: Ent...

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Q: ii) h(x) = e values for the functions along the interva

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Q: 2x5y' = y(3x* + y²) 4

A: Find your answer below 

Q: sec (7x)tan' (7х)dx

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Q: 1. f sin³ 4xcos³4xdz

A: To evaluate the given integral.

Q: Exercise 3. Consider the model economy where the government taxes consumption and uses the tax reven...

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Q: Use the guidelines of this section to sketch the curve. х — 5 f(x) x2

A: f(x)=x-5x2Plotting on graph on corrdinate axes

Q: f(a + h)-f(a) a. Use the definition man = lim to find the slope of the line tangent to the graph of ...

A: The given definition of the slope of the tangent line of a graph at the point P is: mtan=limh→0f(a+h...

Q: 1. |x² In x dx; u = In x, dv = x² dx 2. 0 cos 0 de; u= 0, dv = cos 0 d0 %3D

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Q: z, Z2 Prove

A: If z =x+ iy then  z = x- iy. i2 =-1.

Q: Find the derivative of the function at Po in the direction of u. 3x f(x, y) = tan -1 , P0(-2, 3), u ...

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Q: Use any appropriate method in finding the indicated solution of the following differential equations...

A: As per our guideline we are supposed to be answer only one question you can repost other questions i...

Q: Let A,B be 2x5 matrices, and C a 5x2 matrix. Then(A-3B)C is * O not defined O a 5x5 matrix O a 2x2 m...

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Q: Find an equation for the tangent line to the graph of y = (x° - 4x) .3 at the point (2,0). The equat...

A: Given problem:- Find an equation for the tangent line to the graph of y = (x³ - 4x)10 at the point (...

Q: y

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Q: |e2 sin²(e2«) cos(e24) dx. we let u =e2* To evaluate А) True B False

A: Given:       ∫e2xsin2(e2x)cos(e2x)dx      let u=e2x→du=2e2xdx           =∫sin2ucosu2du            =1...

Q: Ssin( /3x)cos(-2r)dx

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Q: 4. Sketch a graph (different for each) that satisfies the given conditions: a) f'(x) 0 if x -2 (x ...

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Q: Find the first derivative of 2cos(2 + x³). a. -6x² sin(2 + x³) b. -x² (sin 2 + x³) c. -6x² (cos ...

A: daf(x)dx=adf(x)dx ; where , 'a' is constant. dcos (ax)dx =-a.sin(ax) dxndx=n.xn-1 . 

Q: Find the component form of v given its magnitude and the angle it makes with the positive x-axis. ||...

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Q: Sketch the region bounded by the given curves, then find its area. 1. у%3D х*, у%3D2х

A: Since the student has posted multiple questions and does not mention any specific question, so we ar...

Q: Find the vectors that satisfy the stated conditions. NOTE: Enter the exact answers using the provide...

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Q: Consider the surface. z2 = 25y %3D Identify the surface. O cylindrical surface O paraboloid O hyperb...

A: We have to identify the surface z2=25y.

Q: -2 -4 and D = 4 8

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Q: 2n +1 Σ n n tan-1 n n=1

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Q: Find the indefinite integral. (Remember the constant of integration.) | (3 + x + 4e*) dx

A: I=∫ 3+x+4ex dxI=∫3 dx +∫x dx +∫ 4ex dxI=3∫dx +∫x dx +4∫ ex dxI=3x+x22+4 ex +C