Using the definition of the definite integral (as a limit of Riemann sums to evaluate 3 [²₂ (No credit is given for other methods.) 2x² x dx.

Q: 3. lim 3 cos(x) sin(4x) 2x

A: To evaluate the following limit. limx→0 3 cosx sin4x2x

Q: Find an equation for the tangent plane and parametric equations for the normal line to the surface…

A: Given surface is z=e4ysin(4x) and point (π8,0,1)

Q: Value of the integral √₂ = ds where the curve C is given by y = 8√x with 0≤x≤1 is equal to: O…

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Q: A tow truck drags a stalled car along a road. The chain makes an angle of 30 degrees with the road…

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Q: For what point on the curve of y=9x² - 2x is the slope of a tangent line equal to 88?

A: To find a point on the curve with given slope of tangent.

Q: Find a partial fraction decomposition for x+4 x²7x+10 Find a partial fraction decomposition for 2x-3…

A: NOTE: Refresh your page if you can't see any equations. .

Q: Find the divergence of the vector field F. F(x, y) = 2xexi - 6x²y²j

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Q: Find the center of mass of a thin plate of constant density & covering the region bounded by the…

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Q: Use the Shell Method to compute the volume of the solid obtained by rotating the region underneath…

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Q: Find the equation of the tangent line to the curve y = 4 sin a where x = Y . Use exact values.

A: y=4sinx where x=π6we know standard form of equation is y=mx+cwhere m is slope of lined(sinx)dx=cosx…

Q: Find the power series an B and an ∞ Σ anan expansion of if n is even if n is odd. the radius of…

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Q: ticle is located a distance x feet from the origin e in moving it from x = 1 to x = 3?

A: given force  function is f(x) = x2+2x then we have to find work done for x =1  to x =3 work done =…

Q: 4. Exponential Equation is an inequalities involving exponential expression. O True O False

A: An exponential function is a Mathematical function in the form f (x) = ax, where “x” is a variable…

Q: -) Solve (²³=2+1) +1)dx with Composite Simpson's 1/3 Rule for n=4 subintervals.

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Q: The slope of the function's graph at (4,4) is (Simplify your answer.)

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Q: 3. Determine the equation of the parabola with vertex at (1,4) and focus at (1,2).

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Q: Find the absolute extrema of the function on the closed interval. g(x) = 5x² - 30x, [0, 7] minimum…

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Q: Consider the differential equation: dy 9x² dx 9y² - 3 y(2) = 0 A) Solve the differential equation.…

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Q: 9. Below is the graph of f'(x). For what values of x is f(x) decreasing? Explain f'(x) A -1 1 2 3 -2

A: As we know Function decreasing when f'x<0and function increasing when f'x>0

Q: 9. * In 3²x² = 3x+3, O True O False x = -1 and 2/3

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Q: Find the equation of the plane that contains all points that are equidistant from two points…

A: Given that two points A(-1,3,2) and B(8,-2,4) and we find the equation of plane that contains all…

Q: True or False log32x² = log32 + 2log3x O True O False

A: The following properties of log has bben used to solve this question loga×bc=logac+logbc…

Q: b. Consider the following graph of a function g(x). Estimate the following limits (using an answer…

A: Graph of the function is given, we have to find the given limits.

Q: ight, in metres, of an object that has fallen from a height of 180 m is given sition function s(t) =…

A: We will find the required.

Q: Use the shell method to find the volume of the solid generated by revolving the shaded region about…

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Q: 1. Determine the equation of the circle with center at (4,5) and passing through (-1,-7)

A: The center of the circle is:  (h, k) = (4, 5) The circle passing through the point:  x1, y1=-1, -7

Q: 1. * Find the Value of x 7x+4 = 49²x-1 O x=1 O x=2 Ox=3 O x=4 O None of the Above

A: Solution ) 7( x + 4 ) = 49( 2x - 1 )       7( x + 4 ) = 72( 2x - 1 )        [  49 = 72   ] 7( x + 4…

Q: Consider the parametric equations below. x = t2 − 5,    y = 2 − 4t,    −3 ≤ t ≤ 4 Eliminate the…

A: NOTE: Refresh your page if you can't see any equations. . here we have

Q: Assume that X and Y are both differentiable functions of t. Find the required values of dy/dt and…

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Q: m y - 2 y^3-8/2y^2-7y+12

A: Given: limy→2y3-82y2-y+12

Q: Find the area beneath f(x)=x² Inx on the interval [1,2] using the Trapezoidal Rule.

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Q: 21. dx dt4 t = 16 x=t-3/4

A: here we have to find the forth derivative.

Q: Evaluate the integral by first completing the square. (Use C for the constant of integration.) x² +…

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Q: 13. Differentiate the following functions: a)y=e(cosx+sinx) b)y=(x²)2* c) y= tan’(cosx)

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Q: A luxury car runs smoothly on a paved road at 60 mph. If it then decelerates to a stop at a constant…

A: A luxury car runs smoothly on a paved road at 60 mph. If it then decelerates  to stop at a constant…

Q: Find the equation for the plane through the points Po(-2,2,2), Qo (0,2,4), and Ro(3, -2,-4). ...…

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Q: 3. (x+y-4)dx - (3x-y-4)dy = 0; when x = 4, y = 1

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Q: Let f(x) = -5 sin(x) cos(x). df dx d² f dx²

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Q: (a) Find parametric equations for the line that passes through the point (-5, 5) and is parallel to…

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Q: Solve the given differential equation (where the function is subject to the given conditions) by…

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Q: Is -187 9 -18 in the spanning set of Select an answer 2 7 3 2 " -721 6 ? 75

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Q: Let f(x)= This function has: 1) A y intercept at y= A = 2) Roots at A and B, where A < B B = = 2x² +…

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Q: Solve the following differential equation for the initial condition y (0) = -1. Select using the…

A: To solve the following differential equation for the initial condition y0=-1.  By using the…

Q: 20. d4f| dt4 t = 1 f(t) = 6t⁹ - 2t5

A: To find the derivative of given function

Q: Find V × (V × F) if F(x, y, z) = 4xy j + 7xyz k. V x (V x F): =

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Q: Find the particle's velocity and acceleration vectors at t=2, and sketch them as vectors on the…

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Q: Find the volume of the solid generated by revolving the region about the y-axis. The region enclosed…

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Q: Find the volume of the solid obtained by revolving y(x) = sin(5x) for 0 ≤ x ≤ about the x-axis. (Use…

A: Formula used Volume of region obtained by rotating the region about x axis is givan by V = ∫abπy2dx…

Q: ind ted Problem 12: Captain Jack Sparrow has been marooned on an island in the 'Atlantic by his…

A: Given: 19 km east then 8.5 km in direction of8.5 degree north of east

Q: Use cylindrical shells to find the volume of the solid generated when the region enclosed by the…

A: