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QUESTION 5 a) Find and sketch the domain of the function f(x,y) = \n(x2 - y...
2 + (a) Determine and sketch the domain of the function f(x, y) = (x2 +...
2 + (a) Determine and sketch the domain of the function f(x, y) = (x2 + y2 – 4) 9 – (x2 + y2). [7] x6 – yo (b) Evaluate lim (x,y)+(1,1) - Y [5] (c) What does it mean to say that a function f(x, y) has a relative minimum at (a,b)? [4] (d) Find all second order partial derivatives of the function f(x,y) = 22y.
2. Find and sketch the domain of the function f(x,y) = V x2 – y +...
2. Find and sketch the domain of the function f(x,y) = V x2 – y + 2.
QUESTION 5 Consider the function f(x,y) – In19 – x? –y?) X+2 a) Find and sketch...
QUESTION 5 Consider the function f(x,y) – In19 – x? –y?) X+2 a) Find and sketch the domain of the given function. b) Show that the function is continuous at (2-2). (5 marks) (3 marks)
ID Let f(x) = /2x=2 | (a) Find f'(x) as a piecewise function (6) Graph y...
ID Let f(x) = /2x=2 | (a) Find f'(x) as a piecewise function (6) Graph y = f'(x) (c) state the domain of f and the domain of f. Find lin tan 4x cos 3x sin 5x X> 12 Find y if y = (3x+5)*(x+4x) (3 Find y' it ya + 10x tanx 7 Let y= (a) Find (6) Find the equation of the tangent line at (74 y' Elf 8 X3 Prove lim (5-) = 4 (a) write the...
D1.1. Evaluate f'(a) by using the definition of derivative of a function f(x) = 4x2 +...
D1.1. Evaluate f'(a) by using the definition of derivative of a function f(x) = 4x2 + 3x – 5 at a = -2. [4 Marks] D1.2. (a) Find the derivative of y = 4 sin( V1 + Vx). (b) If y = sin(cos(tan(x2 + 3x – 2))), then find the first derivative. [3 Marks] D1.3. Using logarithmic differentiation, find the derivative of y = (sec x)+”.
Answer All Questions. (9) Let f(x,y) = 1+ 4- y2. Evaluate f(3,1), find and sketch the...
Answer All Questions.
(9) Let f(x,y) = 1+ 4- y2. Evaluate f(3,1), find and sketch the domain of f. (10) A thin metal plate, located in the xy-plane, has temperature T(x,y) at the point (x,y). The level curves of T are called isothermals because at all points on such a curve the temperature is the same. Sketch some isothermals if the temperature function is given by 100 T(x, y) = 1 + x2 + 2y2 (11) Show that lim (z2...
calc3 #7 sketch by hand please Find the domain of the function f(x,y) = In(x -y...
calc3 #7
sketch by hand please
Find the domain of the function f(x,y) = In(x -y + 2) and sketch it in the xy-plane.
Show work thumbs up VII. Functions Find the Domain of each function. f(x)--/-x2-4x + 5 g(x)-In(4t-3)...
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VII. Functions Find the Domain of each function. f(x)--/-x2-4x + 5 g(x)-In(4t-3) a) b) e) h(x)- +3x2 -x-3 Find the zeros, vertical asymptotes, and horizontal asymptotes f(x) = 3x"-14x-5 (4x-17x-15 6x2 -7x-5 f(x) = -12 万 b) Transformations a) Beginning with f(x)- Vx, find the function g(x) that shows fcx) shited to the let 2 units, reflected over the x-axis, and then shifted up 7 units. b) Beginning with f(x)find the function g(x) that shows f(x)...
1. Sketch a few of the level curves of the function f(x, y) = surface z...
1. Sketch a few of the level curves of the function f(x, y) = surface z = y2 and then use these to graph the f (x, y) 2. Evaluate the following limits if they exist. If they don't, explain why not. (a lim (x,y)(0,0) + 4y2 x4-y4 (b lim (x,y)(0,0) x2 + y2 cos 2 y2) - 1 lim (c (z,y)(0,0 2ry (x, y)(0,0) Is the function f(x, y) continuous at (0,0)? 3 = (х, у) — (0,0) 2x2y...
Find the domain of each composite function fog , gof if f(x) =3x+1, g(x)=x2
Find the domain of each composite function fog , gof if f(x) =3x+1, g(x)=x2
2 + (a) Determine and sketch the domain of the function f(x, y) = (x2 + y2 – 4) 9 – (x2 + y2). [7] x6 – yo (b) Evaluate lim (x,y)+(1,1) - Y [5] (c) What does it mean to say that a function f(x, y) has a relative minimum at (a,b)? [4] (d) Find all second order partial derivatives of the function f(x,y) = 22y.
2. Find and sketch the domain of the function f(x,y) = V x2 – y + 2.
QUESTION 5 Consider the function f(x,y) – In19 – x? –y?) X+2 a) Find and sketch the domain of the given function. b) Show that the function is continuous at (2-2). (5 marks) (3 marks)
ID Let f(x) = /2x=2 | (a) Find f'(x) as a piecewise function (6) Graph y = f'(x) (c) state the domain of f and the domain of f. Find lin tan 4x cos 3x sin 5x X> 12 Find y if y = (3x+5)*(x+4x) (3 Find y' it ya + 10x tanx 7 Let y= (a) Find (6) Find the equation of the tangent line at (74 y' Elf 8 X3 Prove lim (5-) = 4 (a) write the...
D1.1. Evaluate f'(a) by using the definition of derivative of a function f(x) = 4x2 + 3x – 5 at a = -2. [4 Marks] D1.2. (a) Find the derivative of y = 4 sin( V1 + Vx). (b) If y = sin(cos(tan(x2 + 3x – 2))), then find the first derivative. [3 Marks] D1.3. Using logarithmic differentiation, find the derivative of y = (sec x)+”.
Answer All Questions.
(9) Let f(x,y) = 1+ 4- y2. Evaluate f(3,1), find and sketch the domain of f. (10) A thin metal plate, located in the xy-plane, has temperature T(x,y) at the point (x,y). The level curves of T are called isothermals because at all points on such a curve the temperature is the same. Sketch some isothermals if the temperature function is given by 100 T(x, y) = 1 + x2 + 2y2 (11) Show that lim (z2...
calc3 #7
sketch by hand please
Find the domain of the function f(x,y) = In(x -y + 2) and sketch it in the xy-plane.
Show work thumbs up
VII. Functions Find the Domain of each function. f(x)--/-x2-4x + 5 g(x)-In(4t-3) a) b) e) h(x)- +3x2 -x-3 Find the zeros, vertical asymptotes, and horizontal asymptotes f(x) = 3x"-14x-5 (4x-17x-15 6x2 -7x-5 f(x) = -12 万 b) Transformations a) Beginning with f(x)- Vx, find the function g(x) that shows fcx) shited to the let 2 units, reflected over the x-axis, and then shifted up 7 units. b) Beginning with f(x)find the function g(x) that shows f(x)...
1. Sketch a few of the level curves of the function f(x, y) = surface z = y2 and then use these to graph the f (x, y) 2. Evaluate the following limits if they exist. If they don't, explain why not. (a lim (x,y)(0,0) + 4y2 x4-y4 (b lim (x,y)(0,0) x2 + y2 cos 2 y2) - 1 lim (c (z,y)(0,0 2ry (x, y)(0,0) Is the function f(x, y) continuous at (0,0)? 3 = (х, у) — (0,0) 2x2y...
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