Show the limit x³ y lim (x,y) →(0,0) x6 + y²

Q: Let A(z) represent the area bounded by the graph, the horizontal axis, and the vertical lines at t =…

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Q: A 13 ft ladder is leaning against a house when its base starts to slide away. By the time the base…

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Q: 1) State the order of the given ordinary differential equation. Determine whether the equation is…

A: To state the order of the given ordinary differential equation. To determine whether the equation is…

Q: Solve the exact initial value problem 3y² dx + + (³1²575 2²2 + √²4) · + √2y) dy = 0, y(0) = 2, y5 X…

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Q: Factor each of the operator: SHOW YOUR COMPLETE SOLUTIONS 1.) 2D²5D-3 2.) 3D² + 7D + 2 3.) D³4D²+D+6

A: The factorization is done by splitting the middle term of the quadratic polynomial/operator.

Q: Find the marginal cost function. C(x)=250 +3.5x-0.01x² c'(x) = [

A: we are given the cost function and we need to find out the marginal cost function.

Q: If f(x) = f'(x) = ƒ'(1) = = 2 sin x 3 + cos x > 3 cos (1) () then 3 cos (x) + sin(x) (3 + cos x)² X…

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Q: Consider the following situation. A company purchased computers for each employee and two all-in-…

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Q: (a) Find parametric equations for the line segment that joins the point P(-1, -4,-3) to the point Q…

A: Question no. 1(a):To find the parametric equations for the line segment that joins the point..Note:…

Q: Evaluate the following integral, f (x - 5y) dx - 8y² dy where C' is given by x = y² + 6 from (7, 1)…

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Q: (a) Find parametric equations for the line segment that joins the point P(-1,-4,-3) to the point Q…

A: Question no. 1(a):To find the parametric equations for the line segment that joins the point .Note:…

Q: Find all the second-order partial derivatives of the following function. W = 3x - 2y 2x² + 3y

A: The given function is

Q: Find the marginal cost function. C(x) = 190 +5.7x-0.07x² c'(x) =

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Q: Differentiate the given function. 8 (71 + 1/ ) (71²-9) F(t)= 7t =

A: we need to differentiate the given function.

Q: 2) Find the solution of the given initial value problem in explicit form. Plot the graph of the…

A: As per our guidelines we can answer only 1 question so kindly repost the remaining questions…

Q: Differentiate the following: (a) x² cos(cos(x)) (b) eesin(x)

A: These are different  question  and not sub part of one question,  so we have solved first 2…

Q: Find the derivative of the algebraic function. c5-x5 c5 + x5 f'(x) = f(x) = c is a constant. X

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Q: Find the derivative of the function. y = sin() + sin (9 x) y'(x) = ||

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Q: Q9: Showthat triangle ABC is right at A where A(1,0,1), B(2,1,0), c (1, 2, 3).

A: Question No. (9):To show that triangle ABC is right at A where . Note: Since the student has posted…

Q: If f(x) = f'(x) = f'(4) = tan x - 5 sec x 3x² tan(x) sec(x) X

A: The Quotient Rule:Use the common derivatives:

Q: Find the indicated derivative. for y=x¹5 58 11

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Q: The equation r³+ y³ = 3ry defines a curve named as the Folium of Descartes. (a) Use implicit…

A: The equation  defines a curve named as the Folium of Descartes.By using implicit differentiation to…

Q: dy dx cos(x + y) = 3x Find dy dx dy dx dy dx dy dx = = -3 csc (x + y) - 1 = -3 cos(x + y) - 1 = −3…

A: we need to find out the derivative.

Q: Find the derivative of the trigonometric function. y = sin((πx)8)

A: y=sin⁡((πx)8)

Q: question e,f

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Q: A one-to-one function is given. Write an equation for the inverse function. h(x) = ³√/x-7 0° 8 %6

A: A one-to-one function is given.To write an equation for the inverse function

Q: Evaluate the integral by converting to polar coordinates. 2 √8-y2 S² S Y 1 √1+x² + y² dx dy= = 16pi

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Q: The total cost (in dollars) of producing x food processors is C(x)=2300+60x-0.3x². (A) Find the…

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Q: Solve the following differential equations using HOMOGENEOUS DE. Show your complete solutions. 2.…

A: To solve the following differential equation by using Homogeneous DE.

Q: A volume is described as follows: 1. the base is the region bounded by x = -3 =-y² + 4y + 66 and x =…

A: The base of the solid is bounded by the curves:The intersection points of the curves:Hence, the…

Q: Tel f(x) = at: *+] at x = 2

A: The given function is

Q: Let f(x, y) = x sin(x + y) (a) Calculate the directional derivative of f at the point (1,-1) in the…

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Q: Question 6 Calculate the resultant of the forces shown in the concurrent force system. 6N 40% 30N…

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Q: Consider the following. Find y'(x). y'(x) = y = X = X x² +9 Find the critical numbers of y(x).…

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Q: 7. u = (2, 2), v = (2, −2) 8. u = (2,-2), v = (−2, 2)

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Q: Let L denote the left-endpoint sum using n subintervals. Compute the indicated left sum for the…

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Q: ( 1 lim 5 X→ 2 (2) lim x x → 5 3 lim (2x+5) X→-1

A: You have posted a question with multiple sub-parts, we will solve first three sub-parts for you. To…

Q: Solve 2(cos2x)y' + ysin(2x) = 4cos4x 0 =< x < pi/2

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Q: Evaluate the following limit. Use l'Hôpital's Rule when it is convenient and applicable. lim (15 tan…

A: y=limθ→π2−(15tan⁡θ)15cos⁡θ

Q: Find the slope of the tangent line to the given polar curve at the point specified by the value of…

A: Consider the curve

Q: The graph shows the influence of the temperature T on the maximum sustainable swimming speed S of…

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Q: Show that the function y= x ln x is a solution of the differential equation xy" - y' + (1/x) y = 0.

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Q: - 8x² - 9y², x = cos t, and y = sint, express For the functions w = - dw as a function of t, both by…

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Q: The radius of a right circular cone is increasing at a rate of 1.2 in/s while its height is…

A: given

Q: Determine the velocity of progress with the given equation: D = 20t + 5/t+1 when t = 4 seconds.

A: We have to determine the velocity of progress with the given equation:  when t = 4 seconds.

Q: 5). Find the power series solution to y" + xy = 0, y(0) = 1, y'(0) = 0.

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Q: Evaluate the following integral, S yx² ds where C is given by y x5 for 0<x< 1. =

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Q: Extrema on a sphere Find the points on the sphere x² + y² + z² = 25 where f(x, y, z) = x + 2y + 3z…

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Q: Consider the function f(x) = = 8x² x-6

A: f(x)=8x2x−6

Q: If y xy + x² + 1, then when x = 01/1/12 0 - 12/1/20 O nonexistent O -1 O-2 -1 dy d = ? dx

A: we need to find out the derivative of the function at the given value of x.