Calculus
6th Edition
ISBN: 9781465208880
Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE
Publisher: Kendall Hunt Publishing
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Chapter 11.6, Problem 14PS
To determine
To calculate:To find the directional derivative of the given function at the given point and in the given direction
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Problem 6: (8 points) Find the directional derivative of
f(x, y) = 4x³ 3xy² +0
at the point (1,2) in the direction that has an angle of 7/3 with the positive z-axis.
5.
The position function of a moving object is given by 7(t) = (, et", cos t). Find its velocity
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and acceleration functions.
Question 14
Let T (x, y) represents the temperature at a point (x, y) measured in degrees Celsius.
A bug is crawling on the plane such that its position after t seconds is given by
x = √1+t₁y = 2 + t
where x and y are measured in centimeters.
Given that the derivative of the temperature function at the point (3, 4) is
T (3,4)= 3 and T, (3, 4) = 2.
how fast is the rate of change of temperature with respect to the direction the ant is crawling, 8 seconds after it started crawling?
O 17
5
O
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12
√13
5 pts
Chapter 11 Solutions
Calculus
Ch. 11.1 - Prob. 1PSCh. 11.1 - Prob. 2PSCh. 11.1 - Prob. 3PSCh. 11.1 - Prob. 4PSCh. 11.1 - Prob. 5PSCh. 11.1 - Prob. 6PSCh. 11.1 - Prob. 7PSCh. 11.1 - Prob. 8PSCh. 11.1 - Prob. 9PSCh. 11.1 - Prob. 10PS
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- Find an equation of the tangent line for the following functions at the given points x-2 a. y= at a point (0, -1) x+2 b. y=f(x)3DV2X2 – 7 at a point (4, 5) | c. y=cos(2x) at a point (T, 1) d. y=f(x)=(2x+3)(x³ + 2x + 1) at a point (1, 20) e. x2 + 4xy + y³ = 8 at a point (0, 2)arrow_forwardcompute the derivative. r(1) = (7 – 1, 4 ī, 8)arrow_forwardFind the derivative of the function at the given point in the direction of A. f(x.y.z) = In (x-3y -92). (-3,-3,-3), A= 3i+ 4j 12 O A. 55 6. O B. 55 18 OC. 55 9. O D. 55arrow_forward
- Find the derivative of the following: 1. y = = 5. y 3-2x 3+2x 2. y = (x²+4)²(2x³ — 1)³ - 3. If y = x² - 4x and x = √√2t² + 1, √2 find y'when t = V dy 4. Find given x = y√1-y² = 7. Find A -x 6. Find y" if x³ - 3xy + y³ = 1 dy dx dy given y = 8. Find x² + 2x 9. Find y", given y = given y = u³ +4, u = x x-1 10. Find y", given x² - xy + y² = 3 4√2 a. y' = ¹/2 (5-2√5) 5 b. c. y" dy dx -12 (3+2x)² 4-x 5 4(x-1)2 √1+u, u = √√x gy' = 2x(x² + 4) (2x³ − 1)² (13x³ + 36x - 2) e. y' dy d. = 6x²(x + 2)²(x + 1) dx f. y" h. j. dy dx i. y" = dy dx = = 8x-x3 (4-x²)2 -4xy (y²-x)³ = = B √1-y² 1-2y2 18 (x-2y)² 1 4√x+x√xarrow_forward2. Determine the derivative of g(t) = 8°[(2t + 1)² + t].arrow_forward1 The derivative of the function y = 1 A V2t 1 B 2t/2t 1 2t/2tarrow_forward
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