Question

In: Math

Let F(x, y, z)  =  (6x5 ln(5y2 + 3) + 10z4) i  +  ((( 10yx6)/(5y2 +...

Let F(x, y, z)  =  (6x5 ln(5y2 + 3) + 10z4) i  +  ((( 10yx6)/(5y2 + 3))+ 8z) j  +  (40xz3 + 8y − 6π sin πz) k
and let  r(t)  =  (t3 + 1) i  +  (t2 + 2) j  +  t3k ,  0  ≤  t  ≤  1. Evaluate  

C

F·dr (please explain steps, thank you :)

Solutions

Expert Solution


Related Solutions

Let F(x, y, z) = z tan^−1(y^2)i + z^3 ln(x^2 + 7)j + zk. Find the...
Let F(x, y, z) = z tan^−1(y^2)i + z^3 ln(x^2 + 7)j + zk. Find the flux of F across S, the part of the paraboloid x2 + y2 + z = 29 that lies above the plane z = 4 and is oriented upward.
3. Let F : X → Y and G: Y → Z be functions. i. If...
3. Let F : X → Y and G: Y → Z be functions. i. If G ◦ F is injective, then F is injective. ii. If G ◦ F is surjective, then G is surjective. iii. If G ◦ F is constant, then F is constant or G is constant. iv. If F is constant or G is constant, then G ◦ F is constant.
The curried version of let f (x,y,z) = (x,(y,z)) is let f (x,(y,z)) = (x,(y,z)) Just...
The curried version of let f (x,y,z) = (x,(y,z)) is let f (x,(y,z)) = (x,(y,z)) Just f (because f is already curried) let f x y z = (x,(y,z)) let f x y z = x (y z)
Let F(x, y, z) = z tan−1(y2)i + z3 ln(x2 + 8)j + zk. Find the...
Let F(x, y, z) = z tan−1(y2)i + z3 ln(x2 + 8)j + zk. Find the flux of F across S, the part of the paraboloid x2 + y2 + z = 28 that lies above the plane z = 3 and is oriented upward. S F · dS =
Let F(x,y,z) = < z tan-1(y2), z3 ln(x2 + 1), z >. Find the flux of...
Let F(x,y,z) = < z tan-1(y2), z3 ln(x2 + 1), z >. Find the flux of F across S, the top part of the paraboloid x2 + y2 + z = 2 that lies above the plane z = 1 and is oriented upward. Note that S is not a closed surface.
5. Let X, Y and Z be sets. Let f : X ! Y and g...
5. Let X, Y and Z be sets. Let f : X ! Y and g : Y ! Z functions. (a) (3 Pts.) Show that if g f is an injective function, then f is an injective function. (b) (2 Pts.) Find examples of sets X, Y and Z and functions f : X ! Y and g : Y ! Z such that g f is injective but g is not injective. (c) (3 Pts.) Show that if...
Let f(x,y) be a scalar function, and let F(x,y,z) be a vector field. Only one of...
Let f(x,y) be a scalar function, and let F(x,y,z) be a vector field. Only one of the following expressions is meaningful. Which one? a) grad f x div F b) div(curl(grad f)) c) div(div F) d) curl(div(grad f)) e) grad(curl F)
Let X, Y ⊂ Z and x, y ∈ Z Let A = (X\{x}) ∪ {x}....
Let X, Y ⊂ Z and x, y ∈ Z Let A = (X\{x}) ∪ {x}. a) Prove or disprove: A ⊆ X b) Prove or disprove: X ⊆ A c) Prove or disprove: P(X ∪ Y ) ⊆ P(X) ∪ P(Y ) ∪ P(X ∩ Y ) d) Prove or disprove: P(X) ∪ P(Y ) ∪ P(X ∩ Y ) ⊆ P(X ∪ Y )
Let f(x) = ln x for 1 ≤ x ≤ 3. Write down the formula for...
Let f(x) = ln x for 1 ≤ x ≤ 3. Write down the formula for Simpson's Rule with n = 4 that approximates the integral of ln x on [1, 3]. Without doing numerical calculations, tell whether in approximating the integral of ln on [1, 3] by the Trapezoidal Rule with n = 8, the value T the Trapezoidal Rule gives is larger than, or is smaller than, the integral. Justify your answer.
Let f: X-->Y and g: Y-->Z be arbitrary maps of sets (a) Show that if f...
Let f: X-->Y and g: Y-->Z be arbitrary maps of sets (a) Show that if f and g are injective then so is the composition g o f (b) Show that if f and g are surjective then so is the composition g o f (c) Show that if f and g are bijective then so is the composition g o f and (g o f)^-1 = g ^ -1 o f ^ -1 (d) Show that f: X-->Y is...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT