Calculus Archive: Questions from April 07, 2022
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using the spherical coordinates, x = p sin (phi) cos ( theta), y = p sin (phi) sin (theta), z = p cos (phi) and x ^ 2 + y ^ 2 + z ^ 2 = p ^ 2. The volume of the solid enclosed by the cone z = sqrt (x
10. Para la función fy) - (1, -3/2) es un punto crític maciones es verdadera: A. f(,y) tiene u porque su Hess "SL-Tarde TL,"v1+r+dz dr do B. f(2,y) tien porque su Whendo las coordenadas esféricas,1 answer -
Find dy for the following expressions: dx a) y = x5 ln(3x) b) y = 2 cos(+2x3) X c) 3x2 + 7x + cos (x) y= sin (2x) 2x3y + e2y = 4x + 5x2 y = (2x4 + 4)4x = d) e) =1 answer -
Number 3 please
= In Problems 1-10, the functions are defined for all (x, y) e R². Find all candidates for local extrema, and use the Hessian matrix to determine the type (maximum, minimum, or saddle point). 1. f(x,1 answer -
derivate
9 La derivada de (10 puntos) 5x? y = In O +2 2(1-x) O*-1 OŽI x ܦܐܨ 10 La derivada de: (10 puntos) y = tan(73x) = sen 3x 3x cos? 31 3sen 3x it cos 3x 3 tan 3x sec 3x Ninguna de las anteriores1 answer -
6.if f(X)=(3x2-5x+2)-3/2 then f' (1) is
5 La derivada de: (10 puntos) f (x) = (22-2x)" 2(3x +382-138-12) (x2-2x)" 67-6x2 +26x+24 (x2–2x) 4 -6x3-6x2 +24x+24 (x2–2x) Ninguna de las anteriores 6 Si (10 puntos) f(x) (3x2 – 5x + 2)"} enton1 answer -
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using the spherical coordinates, X = p sin (phi) cos ( theta), y = p sin (phi) sin (theta), z = p cos (phi) and x^2 + y^2 + z^2 = p^2. The volume of the solid enclosed by the cone z = sqrt(x^2 + y^2),1 answer -
Number 9 :)
= = = In Problems 1-10, the tangent plane at the indicated point (xo, Yo, zo) exists. Find its equation. 1. f(x, y) = 2x3 + y2; (1, 2, 6) ) 2. f(x, y) = x2 – 3y2; (1, 2, -11) 3. f(x, y) = xy; (-1,2,1 answer -
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Find the domain of the function f(x,y) = 4x2 + 3y +1. The set of all ordered pairs (x,y) for which: (A) y z 1*48? (B) ys - 1 + $? (C) y > 1443? () y s 14,4x? (E) y > C y> 1447? (D) y s '**' E) y > -141 answer -
find the general solution
Ans. y = c;e - 2x +(°2 - 4x + xyl 19. y" - 4y = 8xe2x 20. y" -- 9y = – 72xe - 3x 21. DID + 1) y e* 22. D'(D - 2)²y = 2ex 23. y + 2y + y = 480 cOS 4x. Ans. y = C, +(c2 + cy* - ***** Ans. y = (c + c1 answer -
find the particular solution using exponential shift
13. (D - 2)2y = 20 -- 3xe2* 14. (D - 2)?y = 4 -- 8x + 6xe2* 15. y" - 9y = 9(2x - 3 + 4xe). 2x + Zer . 16. y" + 4y + 4y = 4x - 6e 17. (D + 1)²y = * + 3x. 18. (D2 - 4)y = 16xe - 2x + 8x + 4.1 answer -
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find the particular solution using exponential shift
13. (D – 2) y = 20 - 3xex. 14. (D - 2)2y = 4 – 8x + 6xe2x 15. y" – 9y = 9(2x - 3 + 4xe).1 answer -
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6. Use the identity tan(a +B) tan a + tan ß 1-tan a tan ß to prove that: tan -1 -1 x + tan Y = tan -1 x + y 1-xy provided --1 answer