Consider the following function. H(x, y) = 7 In(3x²+y³) %3D (a) Find fr(2,3). (b) Find fyy(2,3). (c) Find fry(2,3).

Q: Determine the volume of the solid generated by revolving the region bounded by y = x2 – 4x + 5, the…

A: The given curves are; y=x2-4x+5, x=1, x=4, y=0 x-axis From the given curves the bounded region is as…

Q: The gradient vector for the surface xy + xz + yz = 1 at the point (1, 1,0) is (1, 1,0).

A:

Q: Find the 5th roots of 9. -16/2 + 16vZi

A: =12+32i9De Moivre's theorem;=cosπ3+i sinπ39= eiπ39=ei3π=cos3π + isin3π=-1

Q: 3. (2x + 2)dx 1

A:

Q: Solve using the method of undetermined coefficients y'' - y' + 1/4 y=3 + e^x/2

A:

Q: r = 2sin30 * %3D circle rose inner loop cardioid dimpled convex spiral lemniscate

A: Given problem:- r=2 sin(3θ) To find :-  shape of graph of given polar equation

Q: So, the volume of the solid of revolution is Volume = V = TI (9 - x2)2 dx. To find the volume,…

A:

Q: A ball is launched straight up in the air from a height of 7 feet. Its velocity (feet/second) t…

A:

Q: Use the shell method to write and evaluate the definite integral that represents the volume of the…

A:

Q: 1 0 0 A = -1 2 0 1 0

A:

Q: find the dimensions of the rectangle with the largest perimeter that is inscribed in a circle of…

A:

Q: The average student enrolled in the 20-week Court Reporting I course at the American Institute of…

A: Given function tells us the rate of change in the number of words per minute.

Q: Find functions f (x) and g(x) (either graph or explicit formula) that satisfy both of the following…

A:

Q: 13. ап V21+3п 15. ат — 2" cos пл

A: Follow next step

Q: (1 1x +15x* – 17x³ – 6x² + 7x – 4)dx -3

A:

Q: Q1. Find by implicit differentiation; a) an equation of the normal to the astroid x/3 + y/3 – 4 at…

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: 4. Let f, g be the functions R → R given by 5- 3r if r 1, { if z 5 f(z) = { g(1) = For each of these…

A:

Q: A bicyclist traveling at 14 ft/sec velocity (ft/sec) puts on the brakes to slow down at a constant…

A:

Q: 10x – 2 - dx . (x + 1)(5x² – 2x + 1) 16. Evaluate 5x - A) hx +1|+ n|5x² – 2x + 1|– tan +C 5x- B) Inx…

A:

Q: r = 5 + 2 cos0 : %3D circle rose inner loop cardioid dimpled convex O spiral lemniscate

A: Solution ) limacons  equation  r = a ± b cos θ If  a > b   = dimpled  a = b = cardioid b > a =…

Q: Classify and Solve dy cos x +y sinx = cosx dx

A:

Q: (a) Find an equation of the tangent plane to the surface at the given point. x2 + y2 + z2 = 26, (1,…

A:

Q: Let y be given implicitly as a diferentiable function coev +e -2 -0 then the slope of the tangent…

A:

Q: The velocity of a car is f(t) = 6t meters/sec. Use a graph of f(t) to find the exact distance…

A:

Q: r = 5 + 4sine * circle rose inner loop cardioid dimpled convex spiral lemniscate

A: r= a+b sin x  Is an standard form of cardioid

Q: 5: Evaluate dw/ dt at the given value of t, by using the Chain Rule and by expressing w in terms of…

A:

Q: Determine the location and value of the absolute extreme values of f on the given interval, if they…

A:

Q: : Find the following indefinite integrals.

A:

Q: The gcd of 7544 and 115 is: O 23 O 15 O 3

A:

Q: x – sin 2x -dx x + cos2x

A:

Q: Solve using the method of undetermined coefficients 1/4 y'' + y' + y= x² - 2x

A: Here we have to solve the given differential equation by the method of undetermined coefficients. We…

Q: For the functions f (x) : and g (x) x-4 find the composition f °g and simplify your answer as much…

A: Here, the given functions are: f(x)=1x-4, g(x)=7x

Q: af af Find and ds z when f(x, y) = e*cosy, x= 2s - f and y= 3st. af

A: Given problem:-

Q: The equation p sin(4) coordinates. Enter your answer in the form of an equation. 8 cos(0) is given…

A:

Q: f(x) = e-=/2; [-1,2]

A:

Q: Solve the problem. Determine the dimensions of the rectangle of largest area that can be inscribed…

A: From the figure:Let 2x be the length of the rectangle;Hence,using Pythagoras theorem;width2+2x22…

Q: Find an equation of the tangent plane to the surface at the given point. f(x, y) = x2 – 2xy + y?,…

A: Solving tangent equation

Q: The marginal cost for a company to produce q items is given by MC(q) = 0.003q -0.9q + 600. The…

A:

Q: Evaluate the integral. 3. [(ax-2-4) dx 2.

A: The given integral,        ∫234x-2-4dx

Q: if fcx) : gex) = X 11 X+ 1 find DE n Dg 2.

A:

Q: 10

A:

Q: Let f(x) = 2x + 3/3x-2 , g(x) = 4x/3x − 2, h(x) = √3x − 12, F(x) = 3x + 4, G(x) = 2x − 3 a) Find the…

A: Solve question

Q: There are 17 distinct congruence classes modulo 19. True False

A: we know that from the property of congruence classes    There are exactly n distinct congruence…

Q: dxdy y Vy2-x2

A:

Q: A particle moves along the x-axis with velocity given by v(t) = 2 sin (2t) for time t>0. If the…

A:

Q: equation

A:

Q: Let y be given implicitly as a differentiable function coey + e-2 -0 then the slope of the tangent…

A: Solution is given below...

Q: Confirm that the Integral Test can be applied to the series. Then use the Integral Test to determine…

A:

Q: A particle moves along the x-axis such that at any time t > 0 its position is x(t), its velocity is…

A:

Q: 2. Let g (x, y) = 2a² – y². Compute g (1, 2), g (2, 1), g (1, 1), g(–1, 1), and g (2, –1).

A: