please show all work and statetheorems and definitions used.
Homework Answers
We first show that it's continuous at x=0. For that we use the
definition
Add Answer to:
please show all work and statetheorems and definitions
used.
'sin (E)ff0. Is g differentiable at 0?...
(a) Can there be differentiable functions f,g (on R) with g(0)-f(0) 0 and f()g(x) for all z E R? What about if we ask (only) for continuous functions f,g? (a) Can there be differentiable functio...
(a) Can there be differentiable functions f,g (on R) with g(0)-f(0) 0 and f()g(x) for all z E R? What about if we ask (only) for continuous functions f,g?
(a) Can there be differentiable functions f,g (on R) with g(0)-f(0) 0 and f()g(x) for all z E R? What about if we ask (only) for continuous functions f,g?
please show all work and state theorems and definitions used. Also be available for questions for...
please show all work and state theorems and
definitions used. Also be available for questions for
clarifications that may occur.
uppose R is able at every r T (a,b). Show that |f()- f(b)l Miz - yl for any x,y E (a, b).
please show all work, even trivial steps. Here are definitions if needed. do not write in...
please show all work, even
trivial steps. Here are definitions if needed. do not write in
script thank you!
4. Letf: R2 → R2, by f(x,y) = (x-ey,xy). a. Find Df (2,0). b. Find DF-1(f (2,0)) Inverse Function Theorem: Suppose that f:R" → R" is continuously differentiable in an open set containing a and det(Df(a)) = 0, then there is an open set, V, containing a and an open set, W, containing f(a) such that f:V W has a continuous...
real analysis 1,2,3,4,8please 5.1.5a Thus iff: I→R is differentiable on n E N. is differentiable on / with g'...
real analysis
1,2,3,4,8please
5.1.5a
Thus iff: I→R is differentiable on n E N. is differentiable on / with g'(e) ()ain tained from Theorem 5.1.5(b) using mathematical induction, TOu the interal 1i then by the cho 174 Chapter s Differentiation ■ EXERCISES 5.1 the definition to find the derivative of each of the following functions. I. Use r+ 1 2. "Prove that for all integers n, O if n is negative). 3. "a. Prove that (cosx)--sinx. -- b. Find the derivative...
2. Let f: R R be a continuous function. Suppose that f is differentiable on R\{0} and that there exists an L e R such that lim,of,(z) = L. Prove that f is differentiable at 1-0 with f,(0) = L. (Hint:...
2. Let f: R R be a continuous function. Suppose that f is differentiable on R\{0} and that there exists an L e R such that lim,of,(z) = L. Prove that f is differentiable at 1-0 with f,(0) = L. (Hint: Use the definition of derivative and then use mean value theorem)
2. Let f: R R be a continuous function. Suppose that f is differentiable on R\{0} and that there exists an L e R such that lim,of,(z) =...
Please include a clearly worded explanation and state all theorems and definitions used. PROBLEM # 2...
Please include a clearly
worded explanation and state all theorems and definitions used.
PROBLEM # 2 Let f : [a.b] R be Riemann integrable. a) Show that f is Riemann integrable. b) Show by induction that p(f) is Riemann integrable where p(v)- is any polynomial. c) Let f (laA) c, d and suppose that G : [c, d] → R is any continuous function. Show that the composition G(f) : [a,b] → R is Riemann integrable. (Hint: There are several...
PLEASE SHOW ALL WORK AND EXPLAIN BOTH PARTS. Thanks Let C be the closed curve defined...
PLEASE SHOW ALL WORK AND EXPLAIN BOTH PARTS.
Thanks
Let C be the closed curve defined by r(t) = cos ti + sin tj + sin 2tk for 0 <t< 27. (a) (5 pts) Show that this curve C lies on the surface S defined by z = 2xy. (b) (20 pts) By using Stokes' Theorem, evaluate the line integral / F. dr C where F(x, y, z) = (y2 + cos x)i + (sin y + x2)j + xk
2. Problem 2 Let g(z) be a differentiable function defined on is shown below. Also suppose that g...
2. Problem 2 Let g(z) be a differentiable function defined on is shown below. Also suppose that g(2)-3 realnumbers. The graph of its derivative, g'(z), g'(a) Also define the differentiable, odd function hz) on all real numbers. Some values of h(z) are given below 0 12 3 4 5 h(z 02-42 2 (a) Calculate each of the following quantities or, if there isn't enough information, explain why i. (g'(x) +2) dr i.h() da ii. (h'(z) +2z) dr iv. 8h(x) dr...
show work f(0) = sin 0 and g(0) = cos e. Find the exact valu of...
show work
f(0) = sin 0 and g(0) = cos e. Find the exact valu of the expression below if = 60°. Do not use a calculator. (Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression.)
Question 2 (20 points): Consider the functions f(x, y)-xe y sin y and g(x, y)-ys 1. Show f is differentiable in its domain 2. Compute the partial derivatives of g at (0,0) 3. Show that g is not d...
Question 2 (20 points): Consider the functions f(x, y)-xe y sin y and g(x, y)-ys 1. Show f is differentiable in its domain 2. Compute the partial derivatives of g at (0,0) 3. Show that g is not differentiable at (0,0) 4. You are told that there is a function F : R2 → R with partial derivatives F(x,y) = x2 +4y and Fy(x, y 3x - y. Should you believe it? Explain why. (Hint: use Clairaut's theorem)
Question 2...
(a) Can there be differentiable functions f,g (on R) with g(0)-f(0) 0 and f()g(x) for all z E R? What about if we ask (only) for continuous functions f,g?
(a) Can there be differentiable functions f,g (on R) with g(0)-f(0) 0 and f()g(x) for all z E R? What about if we ask (only) for continuous functions f,g?
please show all work and state theorems and
definitions used. Also be available for questions for
clarifications that may occur.
uppose R is able at every r T (a,b). Show that |f()- f(b)l Miz - yl for any x,y E (a, b).
please show all work, even
trivial steps. Here are definitions if needed. do not write in
script thank you!
4. Letf: R2 → R2, by f(x,y) = (x-ey,xy). a. Find Df (2,0). b. Find DF-1(f (2,0)) Inverse Function Theorem: Suppose that f:R" → R" is continuously differentiable in an open set containing a and det(Df(a)) = 0, then there is an open set, V, containing a and an open set, W, containing f(a) such that f:V W has a continuous...
real analysis
1,2,3,4,8please
5.1.5a
Thus iff: I→R is differentiable on n E N. is differentiable on / with g'(e) ()ain tained from Theorem 5.1.5(b) using mathematical induction, TOu the interal 1i then by the cho 174 Chapter s Differentiation ■ EXERCISES 5.1 the definition to find the derivative of each of the following functions. I. Use r+ 1 2. "Prove that for all integers n, O if n is negative). 3. "a. Prove that (cosx)--sinx. -- b. Find the derivative...
2. Let f: R R be a continuous function. Suppose that f is differentiable on R\{0} and that there exists an L e R such that lim,of,(z) = L. Prove that f is differentiable at 1-0 with f,(0) = L. (Hint: Use the definition of derivative and then use mean value theorem)
2. Let f: R R be a continuous function. Suppose that f is differentiable on R\{0} and that there exists an L e R such that lim,of,(z) =...
Please include a clearly
worded explanation and state all theorems and definitions used.
PROBLEM # 2 Let f : [a.b] R be Riemann integrable. a) Show that f is Riemann integrable. b) Show by induction that p(f) is Riemann integrable where p(v)- is any polynomial. c) Let f (laA) c, d and suppose that G : [c, d] → R is any continuous function. Show that the composition G(f) : [a,b] → R is Riemann integrable. (Hint: There are several...
PLEASE SHOW ALL WORK AND EXPLAIN BOTH PARTS.
Thanks
Let C be the closed curve defined by r(t) = cos ti + sin tj + sin 2tk for 0 <t< 27. (a) (5 pts) Show that this curve C lies on the surface S defined by z = 2xy. (b) (20 pts) By using Stokes' Theorem, evaluate the line integral / F. dr C where F(x, y, z) = (y2 + cos x)i + (sin y + x2)j + xk
2. Problem 2 Let g(z) be a differentiable function defined on is shown below. Also suppose that g(2)-3 realnumbers. The graph of its derivative, g'(z), g'(a) Also define the differentiable, odd function hz) on all real numbers. Some values of h(z) are given below 0 12 3 4 5 h(z 02-42 2 (a) Calculate each of the following quantities or, if there isn't enough information, explain why i. (g'(x) +2) dr i.h() da ii. (h'(z) +2z) dr iv. 8h(x) dr...
show work
f(0) = sin 0 and g(0) = cos e. Find the exact valu of the expression below if = 60°. Do not use a calculator. (Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression.)
Question 2 (20 points): Consider the functions f(x, y)-xe y sin y and g(x, y)-ys 1. Show f is differentiable in its domain 2. Compute the partial derivatives of g at (0,0) 3. Show that g is not differentiable at (0,0) 4. You are told that there is a function F : R2 → R with partial derivatives F(x,y) = x2 +4y and Fy(x, y 3x - y. Should you believe it? Explain why. (Hint: use Clairaut's theorem)
Question 2...
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