Consider F and C below. F(x, y, z) = (2xz + y²)i + 2xyj + (x² + 12z²) k C: x = t², y = t + 3, z = 2t – 1, 0≤t≤1 (a) Find a function f such that F = Vf. f(x, y, z): = =[" C (b) Use part (a) to evaluate Vf. dr along the given curve C.

Q: f= (2xy+ 3x²)ē+ (x² – 2yz + 2y)ē, – (e² + y²)ēz

A: Given

Q: Consider the function P(x) = (x – 2)°(x – 6) - The y-intercept is the point (0,-24) The…

A: Recall: The x intercept is the point where the line crosses the x axis .At this point y=0. The y…

Q: The domain of the function f (x, y) x2+5x+1 is x2 -1 A R? - { (1,y)} B R2 – { (1,y), (-1,y)} C R2 -…

A: Let f:D→E be a function then domain of f is D. Moreover, domain of f is where the function f is well…

Q: a) Consider the function f (x, y) VIn (4 – x² – y²). Find the domain - and range of f(x, y).

A: Solution is given below..

Q: Let f(x, y) = x² + 5y². (a) Find f (5, 1) and f,(5, 1). fx(5, 1) fy(5, 1) =

A: Find

Q: Evaluate L{f(t)} for t+1, t20, t1, t#2 t=1 t=2 (a) f(t)=3, -3,

A:

Q: If f(x, y) = %3D

A:

Q: Locate and classify the local extremum of the function f (x, y) x² + y? – 8x – 2y + 6. | -

A:

Q: For the function, evaluate the following. f(x, y) = x2 – y – xy + 2 (a) f(0, 0) (b) f(1, 0) (с) f(0,…

A:

Q: For the function f(x,y) = 7x² + 6y², find f(x + h,y)-f(x,y) = h f(x+h,y)-f(x,y) h

A:

Q: Consider f(x) = 3|x|, which is in R[-2, 2]. %3D b. Use the function F(x) to find ſ², f.

A:

Q: Find all local extrema of the function f given by f : R? → R, f(x1, r2) = 3x7x2+ x} – 3a? – 3x3 + 2.

A:

Q: The domain of y = v2 – x is A. (-0,2] B. (-0,00) C. (-∞,2) D. [2,0) E. 0

A:

Q: Find the maximum and minimum values of f(x, y)=x+3xy2-3x2-3y²+4.

A:

Q: f :R →R, f(x) = 3 + ax² + bx +11 fonksiyonu (-3,5) aralığında 20 - azalan ise atb-kaçtır ? If the…

A:

Q: For the function f(x,y) = In (7x+2y), find and əx dy

A:

Q: b. Find and sketch the domain of f(x, y, z) = Vz-x² – y²

A: (b) domain of function f(x,y,z) is set of those values of x,y,z where function f(x,y,z) is defined…

Q: Let f(x) = 5- x and g(x) 2, find: a. (fog)(0) b. (go f)(0) = c. (fo g)(x) Preview d. (go f)(x) =…

A: Value of the above ques is

Q: he function f(x)=3x2+2x

A: Introduction: A function is bijective if it is both injective and surjective and a function f(x) is…

Q: 2. In each case, write the function f(z) in the form f(z) = u(x, y) + iv(x, y): z² (a) f(z)=z³+z+1;…

A:

Q: Consider the function f(x, y) = x² – 6x + y? –- 2y + 10. Sketch the domain of the function h defined…

A:

Q: Find f such that f′(x)=8x​, ​ f(4​)=47.

A: Given, f′(x)=8x​,​ f(4​)=47.

Q: Let f(x, y) = √175 – 3x² – 4y² Evaluate f(5,3)

A:

Q: 04 Let f(x) be a contineous function such that Ler - 5/W)dx = = 4 and =9, then a) 81 b) 101

A: Use definite integration property

Q: Ben can wash a car in 2 hours while his younger brother James can do it in 3 hours. How long will it…

A: In 1 hour Ben can wash 12 part of car. in 1 hour his younger brother can wash 13 part of car.

Q: For the function f(x,y) = 3 x³ + 5y4 5 4 x +y find f, fy, f(-1,1), and f,(-3,2).

A:

Q: Determine the antiderivative F of "f" , which is defined by f (x) = 4x3 – 6, where F (0) = 3 %3D

A: Consider the given function fx=4x3-6