Find the unit vector ey, where v = = (4,0,7). (Give your answer using component form. Express numbers in exact form. Use symbolic notation and fractions where needed.) ey =

Q: Use the Shell Method to calculate the volume of rotation, V, about the x-axis for the region…

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Q: Consider a vector field F(x, y, z) = (2xz + y², 2xy, x² + 3z²) and a curve C given by r(t) = (t², t…

A: Consider a vector field F(x, y, z) = <2xz+y^2, 2xy, x^2+3z^2> and a curve C given by r(t) =…

Q: If C(x)= 17,000+600x - 2.8x² + 0.004x³ is the cost function and p(x) = 4,200- 7x is the demand…

A: We have given the cost function C(x) = 17,000 + 600x − 2.8x2 + 0.004x3  and demand function p(x) =…

Q: Sketch the graph of the following parametric equations. a. x = 4, y = sint b. x = e^t, y = e^2t, t ∈…

A: a) x=4 ,y=sint b) x=et,y=e2t ,t∈[0,∞) c)x=3sint,y=4cost ,t∈0,pi

Q: 2 1) Find the area bounded by the curves y = x² and y=√x.

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Q: Find the indefinite integral. (Remember to use absolute values where appropriate. Remember the…

A: we have integration =∫5x2+20.5x3+0.6xdx

Q: Let g(s) es (s³ + 4). 3 a) Find the equation of the tangent line to g at (0,4). y = | b) Find the…

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Q: Use the identity 2 sin x cos x = sin(2x) to find the power series expansion of sin² x at x = 0.…

A: Write the maclaurin series

Q: Use the graph of the rational function f(x) to complete the statement. As x 27, f(x)→ -10 OO -2 +∞ 0…

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Q: Find the following for p =, q =, and r =. Find -2p - r Answer: Submit Answer www.w

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Q: Use Descartes's rule of signs to obtain information regarding the roots of the equation. (Select all…

A: By using Descates's rule of signs to obtain information regarding the  roots of the equation.…

Q: Find the curvature of r(t) = (2t², In(t), t In(t)) at the point (2, 0, 0). K = Need Help? Read it

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Q: Write the component form of the vector shown on the graph below. O O O O Submit Answer

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Q: III. If f\x, y = x² cosy - y. e²y, then find all the second order partial derivatives.

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Q: (5) Compute the following limits directly, without using tables or graphs.. Sh 1 1 (x+h)² x² h (a)…

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Q: Calculate the linear combination. 5(i +2j) - 3(2j+ k) + 7(2k − i) = (x, y, z) (Give your answers as…

A: To calculate the following linear combination. 5i+2j-32j+k+72k-i=x, y, z where,  x=?y=?z=?

Q: Evaluate the definite integral. π/2 x² sin(x) 1 + x8 À -π/2 dx

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Q: Set up an integral for the area of the shaded region. Evaluate the integral to find the area of the…

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Q: use the appropriate limit laws and theorems to determine the limit of the sequence or show that it…

A: We have to find if the given series converges or diverges. For this we will apply ratio test.

Q: 17. bn = 5n-1 12n +9

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Q: ons, use your work (a) to help you the generar (Recall that general antiderivative of a function…

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Q: əz Use the chain rule to find and as əz əs əz at = = əz at z = In(4x + 3y), x = s sin(t), y = t…

A: z=ln4x+3y ,x=s sint ,y=t coss

Q: 6. For what value(s) of k, does the function f(x) = Ae**, where A is some constant, satisfy the…

A: To find the value (s), for which the function fx=Aekx, where A is some  constant, satisfies the…

Q: Use the chain rule to find the indicated partial derivatives. x4. x² + x²y₁ x = s + 2t - u, y = stu…

A: To find partial derivatives of z w.r.t. s,t,u   Given z=x4+x2yx=s+2t-u and y=stu2

Q: Write the vector below in trigonometric form. f =< -√√6, -3v

A: f=&lt;-√6,-3√2&gt; Trigonometric form = ||m||&lt;cosθ,sinθ&gt; m=(vx2+vy2)tanθ=vyvx

Q: (12) Describe each system of planes. If possible, solve the system. a) x + 2y + 3z = 4 2x = y + 4z =…

A: Note:As per our guidelines we are supposed to answer only one question if there are multiple…

Q: The velocity function (in meters per second) is given for a particle moving along a line. v(t) =…

A: we have given velocity function v(t)=5t-9

Q: Find a quadratic equation with the given roots. Write your answers in the form Ax2 + Bx + C = 0.…

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Q: Find the direction in which the maximum rate of change occurs for the function f(x, y) = 3x sin(xy)…

A: To find:  the Direction in which the maximum rate of change occurs for f(x,y)=3xsin(xy) at point…

Q: Show that if f'(x) exists, then we have. lim f(a+h)-f(a-h) = 2f (a) h→0 b

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Q: 1. The graph of f(x) is shown to the right. On the same grid, draw a sketch of f'(x). VA Explain,…

A: Given: Aim:  To draw the sketch of f'(x).

Q: 3. Practice similar Help me with this Find the quotient and remainder using long division for The…

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Q: (ii) (iii) Find the co-ordinates of the turning points of the following function: y = x³ - 6x² +5…

A: Given the equation, we need to find out the turning points of the curve and also where it has maxima…

Q: The equation (5)/(3)log_(4)(x)=9 can be written in the form x=2^(y) for some number y. What is y ?

A: We have to find the value of y. Conversion of log form to exponental formlogbm=x                 →…

Q: Set up an integral representing the area A of the region enclosed by the given curves. y = 5x, y =…

A: The area between the curves y=f(x) and y=g(x) from x=a to x=b is given by the integral…

Q: Find the four second-order partial derivatives. f(x,y) = 3x³y - 5xy + 8y fxx (x,y)= 216x y y (X,Y)=…

A: To find the four second-order partial derivatives. fx, y=3x9y-5xy+8y

Q: Two cars approach an intersection at right angles, one traveling north at 60 km/h and the other…

A: We have to find the rate at which distance between the cars is changing.

Q: 43. an = 2¹/n

A: By using the appropriate limit laws and theorems to determine the limit of the sequence or to show…

Q: Find the rate of change of ƒ (x, y, z) = 6xyz in the direction normal to the surface yx² + xy² + yz²…

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Q: Using the definition of the derivat to find the derivative of the following function. f(x) = x² ;…

A: a) f(x)=x2 b) f(x)=1/2 c) f(x)=sqrt(x) Find the derivative by definition.  According to bartleby…

Q: a. AOR: y = 0 b. AOR: x=0 c. AOR : x = 2

A: Since you posted multiple subparts, I need to solve only first three subparts.

Q: 2 X 2 [√³² L √ ² - ²³ √ x² + ²³² dy da dx 0 X

A: ∫0√2∫x4-x2x2+y2dydx

Q: Find the most general antiderivative of the function. (Check your answer by differentiation. Use C…

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Q: Find the differential of the function. z = x ln(y5 + 2) dz = )dx + ( Jay dy

A: Finding a function's derivative is a step in the mathematical process known as differentiation. The…

Q: e following is not a D.E.? -(z)=0 of the D.E. xdy + ydx = 0 is B. x² + y² = C hose solution is y =…

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Q: In Exercises 39-42, find dy/dx. - Sv V2+cos³ t dt 39. y = 40. y = -7x² [T²³v 2 V2+cos³ t dt

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Q: 6. Given u = a. 5u b. u. V c. [2, -5]and = [-7,2] find

A: Given: v→=-7, 2 To find: v→ Note: Since, the student has mentioned to solve only question 6(c), so…

Q: (c) Given equation r²+(2-1)² = 4 in the cylindrical coordinates. (1) Express the equation in…

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Q: me Value Theorem, which of the following is true?   A) f(x) achieves a maximum f(c) and…

A: f(x)=x2

Q: Find equations of the normal and osculating planes of the curve of intersection of the parabolic…

A: The curve of intersection of the parabolic cylinders x = y2 and z = x2 at the point (1, 1, 1). Find…