Question 12 Find the linear approximation of the function f (x, y) = 2x – y + a²y - near the point (2,0). 2x + 3y + 4 2х + Зу — 4 2а + Зу — 8 2x + 3y

Q: X-7y=-11 ---(1)  5x+ 2y = -18 ---(2)

A: Note:- As statement of problem is missing for given system of equations so we can solve system of eq...

Q: Question 5 dy in terms of x. de 5. Given that y =u² - 4 and u=x +1, find dy dy du hint du de d du dx...

A: Topic:- derivatives   

Q: • Evaluate the following: 1) S (5 cos x - 4 sin x ) dx cos x 2) S dx sin? x 3) S (4 csc x cot x + 3 ...

A: ?As per our company guidelines we are supposed to answer ?️only first 3 sub-parts. Kindly repost oth...

Q: 5. Prove that lim Show your t→-2 t+2 complete solution.

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Q: Find all points (x.y) where f(x.y) has a possible relative maximum or minimum. fx.y) = - 2 + 7xy - 6...

A: We have to find the maxima and minima of the function.

Q: Solve the following equation for x. log5(2x) + log5(3x) = 2

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Q: 4. State the domain and range of the following functions. a) у%3D 5х —4 b) y= Vx-x c) ((x,y)ly = vx²...

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Q: g(b) Use the Substitution Formula, f(g(x)) •g'(x) dx = f(u) du where g(x) = u, to evaluate the follo...

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Q: 2.2) Solve and explain the steps involved. (2+7a)e dr

A: In this question we have to solve Integration.

Q: Solve ſ cot3 4x csc² 4x dx then evaluate the answer at x=22, C=26

A: ∫cot34x csc24x dx

Q: (y – sin? x) dx + sin x dy = 0 2

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Q: Prove the identity It tanh(x) tanh (x), 2x

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Q: If z = x sin y + y sin x a2z then дхду

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Q: Find the area of the shaded region. y 20 (1, 7e) 15 y = 7e* 10 5 y=7xe* X -1.0 -0.5 0.5 1.0 1.5 2.0

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Q: 8. The cost of producing x ounces of gold from a new gold mine is C = f(x) dollars. a) What does f'(...

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Q: A trough is 12 feet long and 3 feet across the top. Its ends are isosceles triangles with altitudes ...

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Q: Write a chain rule formula for the following derivative. for w = f(p, q); p = g(x, y), q = h(x, y) O...

A: We have to find the derivative

Q: Evaluate the integral 1- 25 ds VT- 25 ds

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Q: 3. The sides of a triangle are given as 3x, x+1 and 3x-1. If the perimeter is 56 ft, find the area. ...

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Q: Use integration by parts to evaluate the definite integral. 8t? In(t)dt Give an exact answer

A:     ∫1e8t2lntdt=8·∫1et2lntdt=813t3lnt-3·∫t23dt1e=813t3lnt-3·t391e=813t3lnt-t331e=82e39+19=82e3+19

Q: If z = x? + y?; x = t sin t , y = 2t cos t dz then dt at t = is

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Q: Question 1: The lateral surface of a (right) cone is given by LA = TrVh² + r2 where h is the height ...

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Q: The integral represents the volume of a solid. Describe the solid. 2nx' dx O The solid is obtained b...

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Q: Use the trapezoidal rule with n = 5 to approximate cos(a) - d.x Keep at least 2 decimal places accur...

A: ∫15cos(x)xdx ; n=5

Q: Given the function f'(x) = x(xxt 4)(x – 5)³, what conclusion can be drawn directly from the sign cha...

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Q: 8. 2. k(x) = %3D 1+3e-x first derivative Points of Inflection second derivative concaved up 1. conca...

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Q: A triangle having an area of 22.62 cm2 is inscribed in a circle whose radius is 6 cm. If one of the ...

A: Given query is to find perimeter of the triangle.

Q: Find dx | cos (P) dt y = dx I3D

A: NOTE: Refresh your page if you can't see any equations. . use the integration rule 

Q: (2x -y+2)dy + (x-2y +4)dx =D0

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Q: Use the root test to determine whether the series converges or diverges. If the test is inconclusive...

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Q: You have a wire of length 2 m, which you can bend either into a square or a circle. You also have th...

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Q: The function f is shown below. What is the value of f(x) dx? Write your answer in simplest form. Gra...

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Q: First make a substitution and then use integration by parts to evaluate the integral 6 cos (Vx) dx.

A: In this question we have to solve the integration.

Q: 2. y = log, 3x(x – 4) 3. y = x + 3 In x 4. y = x2 In x

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Q: х+1 dx 3 2 2 25 - x

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Q: 5**+2x (2x3 +1)dx *(2x3+1)dx

A: I have stated the used formulas in the solution.

Q: Write a chain rule formula for the following derivative. for w = f(p, q, r); p = g(t), q = h(t), r =...

A: Here, w=f(p,q,r), p=g(t), q=h(t) & r=k(t) So, 

Q: The region bounded by the given curves is rotated about the specified axis. Find the volume of the r...

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Q: Evaluate the following integrals of inverse trig functions. NOTE: SHOW COMPLETE SOLUTIONS 1.∫ sin^...

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Q: Determine the maximum and minimum points of the given functions below. f(x) = 3x4 – 16x3 + 24x2

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Q: For the following composite function, find an inner function u = g(x) and an outer function y =f (u)...

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Q: The volume of. a cube decreases at a rate of 0.5 ft?/min. what is the rate of change of the side len...

A: Application of derivative

Q: Find the limit of the function along the path y = 2x X-1 lim (x.y)-(0,0) y -1

A: We have to find the limit of the function along the path

Q: Question 2 We consider compound interest with a nominal annual rate r compounded n times per year. T...

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Q: Find the volume formed by rotating about the y-axis the region enclosed by: 10y and y° = x with y > ...

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Q: The integral -8 sin(x) cos(x) dx can be evaluated in four different ways: (1) The substitution u cos...

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Q: Use the method of cylindrical shells to find the volume generated by rotating the region bounded by ...

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Q: Let h(x) = f(g(x)) and p(x) = g(f(x)). Use the table below to compute the following derivatives. a. ...

A: h(x)=fgx and px=gfx

Q: Given the function f(x) = x* – 24x², determine all intervals on which f is both decreasing and conca...

A: In this question we have to determine all intervals on which f is both decreasing and concave down.

Q: cos° Vx dx x CsC csc Va

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