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Q: Suppose that the intersection of the graph of z=f(x,y) with the plane x =1 is a parabola that open ...

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Q: Show that 1+1/x+1/x2+1/x3+1/x4+…=x/x−1 assuming x>1.

A: Given series is, This a GP series.

Q: Replace the polar equations with equivalentCartesian equations. Then describe or identify the graph....

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Q: write the function in the form y = ƒ(u) and u = g(x).Then find dy/dx as a function of x. = 5 cos-4 x

A: Given: y=5cos(-4x) Here y=5cosu, and u=-4x.

Q: A cylindrical water tank 4 meters high with a radius of 2 meters is located on a tower so that the b...

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Q: Show that the polar equation r = a sin θ + b cos θ where ab ≠ 0 represents a circle, and find its...

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Q: How are triple integrals defined in cylindrical and spherical coor-dinates? Why might one prefer wor...

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Q: write a formula for ƒ . g . h ƒ(x) = x + 1, g(x) = 3x, h(x) = 4 - x

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Q: find the areas of the surfaces generated by revolvingthe curves about the given axes. y = x3/3, 0 ≤ ...

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Q: calculate the integral.

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Q: The sum to infinity of a GP is twice the sum of the first two terms. Find possible values of the com...

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Q: Test for symmetry with respect to each axis and to the origin y = 9x − x2

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Q: please explain and show all parts

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Q: Sketch the graph of the equation by point plotting y = 1/(x + 2)

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Q: calculate the integral.

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Q: Find an antiderivative of the function f(x)=e2x.

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Q: say whether the function graphed is continuous on[-1, 3]. If not, where does it fail to be continuou...

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Q: A drilling machine is to have 8 speeds ranging from 100 rev/min to 1000 rev/min. If the speeds form ...

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Q: Find the integral ∫dx / sinx+cosx+1

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Q: The equation for the moment about the origin of a one-dimensional system is M0 = 5(−3) + 2(−1) + 1(1...

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Q: Perform the indicated operations. Simplify the result.

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Q: Determine whether each integral is convergent ordivergent. Evaluate those that are convergent integ...

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Q: Use the graph of the function f to decide whether the value of the given quantity exists. (d) l...

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Q: -3 -2 -1 1 2 0000000 3.

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Q: Use separation of variables to find the general solution of the differential equation. dr 0.03r ds

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Q: Could you help me with this question? I'm not sure how to solve for the values. I'd appreciate the h...

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Q: = 1 + 16 9. revolving (#1) Find the volume of the solid bounded by about the x-axis:

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Q: Consider the spiral given parametrically by x( t ) = 4 e−0.2 t sin( 2 t ) y( ...

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Q: Find the volume of the solid enclosed by the cone z = sqrt(x2 + y2) between the planes z = 1 and z =...

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Q: Calculus Question

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Q: Line integrals of vector fields in the plane Given the followingvector fields and oriented curves C,...

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Q: Consider a rectangle with perimeter 28 (units). Let the width of the rectangle be w (units) and let ...

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Q: Find all points of intersection of the graphs of x2 − y = 3 and x − y = 1

A: To find the points of intersection, we solve both equations.

Q: Find the integral ∫e−xsinxdx.

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Q: evaluate the integral using the appropriate method or combination of methods covered thus far in the...

A: Here given Now substitute as

Q: Find the general indefinite integral. ∫ (√ x3+ 3√ x2) dx

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Q: Among all the points on the graph of z = 10 - x2 - y2 that lie above the plane x + 2y + 3z = 0, find...

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Q: Find all the second partial derivatives. w = u9 + v9 wuu = wuv = ...

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Q: Show that 13x - 12 can be made as small as desired by taking x close to 4. lim (7x - 4) = 10x➔2

A: Let . Domain of f(x) is R and limit of the function is two. The limit of the function is a real numb...

Q: Find the indicated partial derivative. f(x, y) = x3y9; fx(5, −1) fx(5, −1) =

A: Partial differentiation of a function with respect to a specified variable can be evaluated by consi...

Q: Solve inequality. Use interval notation to express solution sets and graph solution set on a numbe...

A: Adding 9 on both sides, we get Adding 4x on both sides, we get Dividing by 10 on both sides, we ge...

Q: If the sides of a rectangular solid are as shown, and = 4, determine the angle, 0, between the diago...

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Q: The rate of change (in thousands of units per year) in sales S of a biomedical syringe is modeled by...

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Q: Suppose that the differentiable function y = ƒ(x) has an inverse and that the graph of ƒ passes thro...

A: Write the equation of line in the slope-intercept form using point (2,4) and slope 1/3.

Q: Use a graphing utility to find the points of intersection of the graphs of the equations. Check your...

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Q: Graph the functions in Exercises 23–26 in the ts-plane (t-axis horizontal, s-axis vertical). What is...

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Q: Calculus Question

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Q: Which of the following integrals are improper? Why? integral 0 to pie / 4 tan x dx

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Q: Find the average distance from a point P(x, y) in the disk x2 + y2<=a2 to the origin.

A: Average distance is given as

Q: please explain and show all parts

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Transcribed Image Text

51. Compute x² _ and then using the identity dx in two ways and verify that the answers agree: first via trigonometric substitution х2 — 1 x +1