Evaluate √80 22² x²e-x² dx.

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Q: 2. The position of a rider on a Ferris wheel is an example of periodic motion. Find three other…

A: 1 )A Rocking Chair

Q: Evaluate the definite integrals (show your solutions) sẽ có cos³ 3xsin3xdx

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Q: what is math

A: Definition of mathematics

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Q: Calculate the double integral S fæ cos(2x + y) dA where R is the region: 0 ≤ x ≤ 7,0 ≤ y ≤ 4

A: The given integral is: ∫∫R x cos(2x+y) dA       where R is the region:  0≤x≤π6,   0≤y≤π4

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Q: SO S integral by reversing the order of integration. 1. Sketch the region of integration for X 1+y5…

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A: Given query is to find the interval where function increasing and decreasing

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Q: Find the maximum and minimum values of the function f(x, y) = e subject to x³ + y³ = 54 Please show…

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Q: Find the slope of the following lines.

A: see below the answer and calculation

Q: 1. Evaluate the following integrals: b. I sin(4x) cos² (3x) dx

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Q: analyze the function f(x) = * +19 if <10 I 2 10 z +14 if # 2 10

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Q: Determine the convergence or divergence of the series and identify the test used. Σ η = 1 1 3-2

A: The given series is  convergent .Solution is given below.

Q: A water tank in the shape of an inverted circular cone has a base radius of 2 m and height of 3 m.…

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Q: Consider the solid obtained by rotating the region bounded by the given curves about the y-axis. x =…

A: The given region is:x=33y ,      x=0    and     y=2

Q: Question 1 [ a) [ b). Consider the function f(x)=x²+3x+c Find the domain of f(x) in terms of c on…

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Q: 6. (a) Let f(x) g(x) = k 4- x Find lim f(x), lim f(x), and lim f(x). Find k so that f(x) is…

A: (a).The given function is:f(x)=x2+2               x&lt;1kx=14-xx&gt;1

Q: 3. Find the differential equation by eliminating the arbitrary y = (x+c)ex constant State the…

A: The given solution of the differential equation y=x+ce-x. We have to find the differential equation…

Q: Find the equation of the line tangent to the graph of f(x)=(lnx)2 at x=9.

A: Given query is to find the equation of the tangent line.

Q: Use a geometric series or the nth-Term Test to determine the convergence or divergence of the…

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Q: Replace ​? with an expression that will make the equation valid.   d/dx (3 − 4x2 ) 5= 5 (3 − 4x2 )4…

A: let y=(3-4x2)5

Q: Graph the line with the given point and slope.

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Q: intervals on which the graph of f is concave​ upward, the intervals on which the graph of f is…

A: Given query is to find concavity of the graph and inflection points.

Q: Consider the solid obtained by rotating the region bounded by the given curves about the line x = 3.…

A: figure:-

Q: Determine whether the integral is convergent or divergent. 3 36 √3-x O convergent O divergent dx If…

A: Given integral:- ∫23363-xdx

Q: Find the gradient of the function y at x = 4.

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Q: (a) Prove that F(x, y, z) = (y² cos r+z³)i+(2y sin r-4)j+(3r2+2)k is a conservative vector field.…

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Q: How much must be invested at the beginning of each year at 12%, compounded annually, to pay off a…

A: It is given that  We need to invest some money at the beginning of each year at 12%, compounded…

Q: b) Polar equation r = √2rcos0 - 7 to a Cartesian equation.

A: Given Equation:- r=2rcosθ-7

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Q: 1. What does it mean to say that a function is periodic?

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Q: K A Coast Guard Station Able is located L=200 miles due south of Station Baker. A ship at sea sends…

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Q: dy (y-1)√y²-2y-3 S.

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Q: Fill in the missing values to make the equations true. (a) log, 3 + log, 8 = log, 5 (b) log₂ 5 -…

A: Given Equations:- log53+log58=log5 log25-log2=log257 log325=log35

Q: Find the​ equation(s) of the tangent​ line(s) to the graph of the indicated equation at the​…

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Q: Solve: dy/dx = −(y − 27) ^2/3 , with y(0) = 91. Express your answer as y=f(x).

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Q: Consider the function f(x) below. At what value(s) of x are the inflection points? Enter answer…

A: for inflrction points  put   f''(x)=0d dx(xn)=nxn-1d dx(constant)=0

Q: Solve the following differential equation: [e2y − y cos(xy)]dx + [2xe2y − x cos(xy) + 2y]dy = 0

A: e2y − y cosxydx + 2xe2y − x cosxy + 2ydy = 0

Q: [6 6x ln (x + 5) dx

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Q: 2y dx (1-y)' 7

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Q: (a) A water container, whose circular cross section is 6 ft in diameter and whose height is 8 ft, is…

A: Given:    A = area of the tank a = area of bottom hole…

Q: 4. Let (n) be an increasing sequence of real numbers. Assume, furthermore, that (x₂) has a…

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Q: Find the value of f'(9) if f(t) = 10√t - 7 √t

A: Here is the solution:

Q: Evaluate the following limit using L'Hospital's rule. Provide your answer below: lim (cos(9x))(+2)…

A: d dx(lnx=1xd dx(cosx)=-sinxd dx(xn)=nxn-1sinxcosx=tanx

Q: Use Newton's method to find the slope of the tangent to the curve defined as y = -5x² + 2x-7

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Q: Convert the following standard form to general form of parabola. a. (y+1)²=-2(x+2)

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: how do we know xi = 1 + 2i/n

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Q: Find the domain of the function using interval notation. f(x) = -2x (x-2)(x-7) To enter oo, type…

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