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1. For all x, the function f(x) = tan-',+ cot-1, has derivative f'(z)-12-17 0 1 +22...
3 12 Smaller Triangle Larger Triangle sin = sin = cos = cos = tan 0=...
3 12 Smaller Triangle Larger Triangle sin = sin = cos = cos = tan 0= tan (= CSC = CSC = sec = sec = cot 8 = cot = Explain why the function values are the same. The triangles are similar so corresponding sides are proportional. The triangles are congruent so the trigonometric function values must be the same.
Show that the real and imaginary parts of the complex-valued function f(x) = cot z are...
Show that the real and imaginary parts of the complex-valued function f(x) = cot z are - sin 2.c sinh 2g u(I,y) v(x,y) = cos 2x - cosh 2y cos 2x - cosh 2y (cot 2 = 1/tan 2)
real analysis 4. Let f(x) = tan x = suur on (, ). Note that f...
real analysis
4. Let f(x) = tan x = suur on (, ). Note that f is continuous. (a) Sketch the graph of f. (b) Find f'(2). (c) Explain why f is strictly increasing. So f has an inverse function, f-'(x) = arctan x. (d) Sketch the graph of arctan r. (e) Find the derivative of arctan z. Show all your work.
(a) A function / has first derivative f'(z) = and second derivative 3) f"(x) It is also known that the function...
(a) A function / has first derivative f'(z) = and second derivative 3) f"(x) It is also known that the function f has r-intercept at (-3,0), and a y-intercept at (0,0) (i) Find all critical points, and use them to identify the intervals over which you will examine the behaviour of the first derivative ii) Use the f'(), and the First Derivative Test to classify each critical point. (ii) Use the second derivative to examine the concavity around critical points...
Consider the complex functions given below: a) f(z) z,(z # 0) b) f(z)1, (0) c) f()22...
Consider the complex functions given below: a) f(z) z,(z # 0) b) f(z)1, (0) c) f()22 d)f(2)1/(z+1), (z ) Verify that the Cauchy-Riemann equations are satisfied, and evaluate f (z) expression using the basic definition of derivative operation based on the limiting case as lim Az-0
Consider the complex functions given below: a) f(z) z,(z # 0) b) f(z)1, (0) c) f()22 d)f(2)1/(z+1), (z ) Verify that the Cauchy-Riemann equations are satisfied, and evaluate f (z) expression using the basic...
12. Determine the derivative of the function. f(x) = (x - 1)e7x + 6 a. f'(x)...
12. Determine the derivative of the function. f(x) = (x - 1)e7x + 6 a. f'(x) = 27x+6(7x – 6) b. $'(x) = 27x+617x + 6) C. $'(x) = 7e7x+6(x - 1) d. f(x) = _ 3x+47 – 6X2x + 6) Inx 13. Determine the derivative of the function. 1. sm) = 1-31(c) b. f'(x) = Lt nec. Sw)= d. S(0) = . sm)= Blanket
Consider the complex functions given below: a) f(z) z,(z # 0) b) f(z)1, (0) c) f()22...
Consider the complex functions given below: a) f(z) z,(z # 0) b) f(z)1, (0) c) f()22 d)f(2)1/(z+1), (z ) Verify that the Cauchy-Riemann equations are satisfied, and evaluate f (z) expression using the basic definition of derivative operation based on the limiting case as lim Az-0
5. [12 Marks) Consider the level surface of the function f(x, y, z) defined by f(x,...
5. [12 Marks) Consider the level surface of the function f(x, y, z) defined by f(x, y, z) = x2 + y2 + x2 = 2a?, (1) where a is a fixed real positive constant, and the point u = (0,a,a) on the surface f(x, y, z) = 2a. a) Find the gradient of f(x, y, z) at the point u. b) Calculate the normal derivative of f(x, y, 2) at u. c) Find the equation of the tangent plane...
attempted, please help! OnCALTOA 9. (12pts) Find all the trig function values for each angle. cost=-3/5, with tan 1<0 a. sin6--3/5 and tan 0--3/ b. CSC sece cos sec / tan3 cot cot 10(4pts)Find...
attempted, please help!
OnCALTOA 9. (12pts) Find all the trig function values for each angle. cost=-3/5, with tan 1<0 a. sin6--3/5 and tan 0--3/ b. CSC sece cos sec / tan3 cot cot 10(4pts)Find the exact value of sin (tan-
OnCALTOA 9. (12pts) Find all the trig function values for each angle. cost=-3/5, with tan 1
using discrete structures 3. Consider the function F(x, y, z) for x, y, z z 0 defined as follows: a. F(x, y, 0)-y+1 b. F(x, 0, 1)-x c, F(x, 0, 2) = 0 d. F(x, 0, z+ 3)-1 e. F(x, y, z)-F(x, F(x, y-1, z...
using discrete structures
3. Consider the function F(x, y, z) for x, y, z z 0 defined as follows: a. F(x, y, 0)-y+1 b. F(x, 0, 1)-x c, F(x, 0, 2) = 0 d. F(x, 0, z+ 3)-1 e. F(x, y, z)-F(x, F(x, y-1, z), z-1) Using Induction, prove the following a. F(x, y, 1)-x +y b, F(x, y, 2) = xy c. F(x, y, 3)-xy
3. Consider the function F(x, y, z) for x, y, z z 0 defined...
3 12 Smaller Triangle Larger Triangle sin = sin = cos = cos = tan 0= tan (= CSC = CSC = sec = sec = cot 8 = cot = Explain why the function values are the same. The triangles are similar so corresponding sides are proportional. The triangles are congruent so the trigonometric function values must be the same.
Show that the real and imaginary parts of the complex-valued function f(x) = cot z are - sin 2.c sinh 2g u(I,y) v(x,y) = cos 2x - cosh 2y cos 2x - cosh 2y (cot 2 = 1/tan 2)
real analysis
4. Let f(x) = tan x = suur on (, ). Note that f is continuous. (a) Sketch the graph of f. (b) Find f'(2). (c) Explain why f is strictly increasing. So f has an inverse function, f-'(x) = arctan x. (d) Sketch the graph of arctan r. (e) Find the derivative of arctan z. Show all your work.
(a) A function / has first derivative f'(z) = and second derivative 3) f"(x) It is also known that the function f has r-intercept at (-3,0), and a y-intercept at (0,0) (i) Find all critical points, and use them to identify the intervals over which you will examine the behaviour of the first derivative ii) Use the f'(), and the First Derivative Test to classify each critical point. (ii) Use the second derivative to examine the concavity around critical points...
Consider the complex functions given below: a) f(z) z,(z # 0) b) f(z)1, (0) c) f()22 d)f(2)1/(z+1), (z ) Verify that the Cauchy-Riemann equations are satisfied, and evaluate f (z) expression using the basic definition of derivative operation based on the limiting case as lim Az-0
Consider the complex functions given below: a) f(z) z,(z # 0) b) f(z)1, (0) c) f()22 d)f(2)1/(z+1), (z ) Verify that the Cauchy-Riemann equations are satisfied, and evaluate f (z) expression using the basic...
12. Determine the derivative of the function. f(x) = (x - 1)e7x + 6 a. f'(x) = 27x+6(7x – 6) b. $'(x) = 27x+617x + 6) C. $'(x) = 7e7x+6(x - 1) d. f(x) = _ 3x+47 – 6X2x + 6) Inx 13. Determine the derivative of the function. 1. sm) = 1-31(c) b. f'(x) = Lt nec. Sw)= d. S(0) = . sm)= Blanket
Consider the complex functions given below: a) f(z) z,(z # 0) b) f(z)1, (0) c) f()22 d)f(2)1/(z+1), (z ) Verify that the Cauchy-Riemann equations are satisfied, and evaluate f (z) expression using the basic definition of derivative operation based on the limiting case as lim Az-0
5. [12 Marks) Consider the level surface of the function f(x, y, z) defined by f(x, y, z) = x2 + y2 + x2 = 2a?, (1) where a is a fixed real positive constant, and the point u = (0,a,a) on the surface f(x, y, z) = 2a. a) Find the gradient of f(x, y, z) at the point u. b) Calculate the normal derivative of f(x, y, 2) at u. c) Find the equation of the tangent plane...
attempted, please help!
OnCALTOA 9. (12pts) Find all the trig function values for each angle. cost=-3/5, with tan 1<0 a. sin6--3/5 and tan 0--3/ b. CSC sece cos sec / tan3 cot cot 10(4pts)Find the exact value of sin (tan-
OnCALTOA 9. (12pts) Find all the trig function values for each angle. cost=-3/5, with tan 1
using discrete structures
3. Consider the function F(x, y, z) for x, y, z z 0 defined as follows: a. F(x, y, 0)-y+1 b. F(x, 0, 1)-x c, F(x, 0, 2) = 0 d. F(x, 0, z+ 3)-1 e. F(x, y, z)-F(x, F(x, y-1, z), z-1) Using Induction, prove the following a. F(x, y, 1)-x +y b, F(x, y, 2) = xy c. F(x, y, 3)-xy
3. Consider the function F(x, y, z) for x, y, z z 0 defined...
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