Given F(x, y, z) = e² i + (xe³ + e²) j+ ye² k.(a) Show that F is conservative by finding curl F.(b) Find a potential function f such that F = Vƒ.(c) Evaluate the lineintegralintegral0 ≤ t ≤ π/2.F. dr where C is given by r(t) = 3 costi+tj + 3 sint k,

use the fundamental theorem of calculus and partial derivative for finding the line integral.

Answered: Given F(x, y, z) = ei + (xe + e*)j +…

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter7: Integration

Section7.5: The Area Between Two Curves

Problem 21E

See similar textbooks

Similar questions

find curl (curl F) = V x (V X F).
a) Find the potential function of F(x,y)=(5+8xy²,8x*y), i.e. a function o, so F = Vo b) Use the potential function found above and the Fundamental Theorem of Calculus to evaluate F· dr where the curve Cis r(t)=(t,-),1
Evaluate C F · dr using the Fundamental Theorem of Line Integrals. Use a computer algebra system to verify your results. (2yi C + 2xj) · dr C: smooth curve from (0, 0) to (2, 3) Please explain each step. I am getting confused.
b) Find the directional derivative (D.) of the function at P in the direction of PQ f (r, y) = sin 2x cos y, P(T, 0), Q()
Does f(z)=z/(sin z)^2 have a pole of order 1 or 2 at z=0?
1. Let R and b be positive constants. The vector function r(t) = (R cost, R sint, bt) traces out a helix that goes up and down the z-axis. a) Find the arclength function s(t) that gives the length of the helix from t = 0 to any other t. b) Reparametrize the helix so that it has a derivative whose magnitude is always equal to 1. c) Set R = b = 1. Compute T, Ñ, and B for the helix at the point (√2/2,√2/2, π/4).
1. Consider the vector-valued function F(t) = sin(2t) t (2, 1, -2), a) Find the domain of F. b) Show that F is continuous at t = 0. ; et, t 1-√1+t, t #0 t = 0. = (1/2/3/17, -2). 2. Consider the vector-valued function R(t) with R(1) = (1,2,−1) and R (t) = (1 a) Find '(1) if (t) = (-2, -3t, t²) × R'(t). b) Find the equation of the normal plane to the graph of Ả at t = 1. c) Find the arc length of the graph of R from the point at t = 1 to the point at t = 3. d) Find the curvature of the graph of R at t = 1.

Recommended textbooks for you

Calculus For The Life Sciences

Calculus

ISBN:

9780321964038

Author:

GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:

Pearson Addison Wesley,

Calculus For The Life Sciences

Calculus

ISBN:

9780321964038

Author:

GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:

Pearson Addison Wesley,

SEE MORE TEXTBOOKS

Given F(x, y, z) = ei + (xe + e*)j + ye² k. (a) Show that F is conservative by finding curl F. (b) Find a potential function f such that F = Vf. So (c) Evaluate the line integral 0 ≤t≤ π/2. F. dr where C is given by r(t) = 3 costi+tj+ 3 sint k,