CALCULUS W/SAPLING ACCESS >IC<
4th Edition
ISBN: 9781319323394
Author: Rogawski
Publisher: MAC HIGHER
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Chapter 15.5, Problem 25E
To determine
The directional derivative of in the direction at the point .
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Find the direction in which the maximum rate of change occurs for the function
f(x, y) = 4x sin(xy) at the point (1,5). Give your answer as a unit vector.
(sin(5) + 5 cos(5))i + cos(15) i
1+ (5 cos (5))² + 10 sin(5) - cos (5)
x Invalid notation. syntax incomplete.
State the rules for differentiating and integrating vector functions. Give examples.
Compute the directional derivative in the direction of v at the given point.
f(x, y) = e*y-y,
v = (12, –5),
P = (-1,–1)
Remember to use a unit vector in your directional derivative computation.
(Give an exact answer. Use symbolic notation and fractions where needed.)
Duf(-1, –1) =
Chapter 15 Solutions
CALCULUS W/SAPLING ACCESS >IC<
Ch. 15.1 - Prob. 1PQCh. 15.1 - Prob. 2PQCh. 15.1 - Prob. 3PQCh. 15.1 - Prob. 4PQCh. 15.1 - Prob. 5PQCh. 15.1 - Prob. 1ECh. 15.1 - Prob. 2ECh. 15.1 - Prob. 3ECh. 15.1 - Prob. 4ECh. 15.1 - Prob. 5E
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- Compute the directional derivative in the direction of v at the given point. S(x, y) = xy – x, v=i-j, P= (-1,2) Remember to use a unit vector in your directional derivative computation. (Give an exact answer. Use symbolic notation and fractions where needed.) Duf(-1,2) = -22 Incorrectarrow_forwardIn Exercises 21-30, calculate the directional derivative in the direction ofv at the given point. Remember to use a unit vector in your directionalderivative computation.arrow_forwardCompute the directional derivative in the direction of v at the given point. S(x, y) = e*}-°, v= (12,–5), P= (3,3) Remember to use a unit vector in your directional derivative computation. (Give an exact answer. Use symbolic notation and fractions where needed.) Du S(3, 3) =arrow_forward
- ry. The directional derivative of f )in the directional (6, 2 and at the point (2, y) - (6,- 4) is Question Help: OVideo Submit Questionarrow_forward= Calculate the directional derivative of g(x, y, z) z² - xy + 3y² in the direction v = (1, -6,4) at the point P = (2, 1, −3). Remember to use a unit vector in directional derivative computation. (Use symbolic notation and fractions where needed.) Dvg(2, 1, -3) =arrow_forwardCompute the directional derivative in the direction of v at the given point. f(x, y) = e*y-y°, (12, –5), P = (4,4) V = Remember to use a unit vector in your directional derivative computation. (Give an exact answer. Use symbolic notation and fractions where needed.) Du f(4, 4) =arrow_forward
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- Use the contour diagram of f to decide if the specified directional derivative is positive, negative, or approximately zero. ? 1. At the point (-2, 2) in the direction of i, 2.4 v 2. At the point (1,0) in the direction of –i, 1.6 0.8 v 3. At the point (–1, 1) in the direction of (-i + j)//2, 아 ? 4. At the point (0, 2) in the direction of j, 0.8 5. At the point (0, –2) in the direction of (i – 2j)//5, -1.6 4.0 8.0 v 6. At the point (-1,1) in the direction of (-i – j)/V2, -2.4 2.4 -1.6 -0.8 0.8 1.6 2.4 (Click graph to enlarge) 12.0 10.0 12.0 10.0 6.0 10.0 12.0 10.0 12.0 >arrow_forwardCompute the directional derivative in the direction of v at the given point. f(x. y) = xy - x, v=i-j. P= (-1,2) Remember to use a unit vector in your directional derivative computation. (Give an exact answer. Use symbolic notation and fractions where needed.) Du f(-1,2) = 22 Incorrectarrow_forwardFind the directional derivative of the function at the given point in the direction of the vector v. fx, y, z) = V xyz, (2, 2, 9), v = (-1, -2, 2) Pu(2, 2, 9) = Need Help? Read Itarrow_forward
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