1. Find the rate of change of the temperature at the point P = (2, –2, 2) in the direction toward the point Q = (3, -4, 3). f(2, -2, 2) = PQ Answer: D. 2. In what direction does the temperature increase fastest at P? Answer: 3. Find the maximum rate of increase at P. Answer:

Q: Solve for the Slope and Rate of Change of the following. 1. What is the slope of the graph y = -x2…

A: As per bartleby guidelines we are supposed to answer only 3 subparts per question. This post has 4…

Q: 10) At t = 55 seconds, an object moving along a straight path is 47 meters from its origin. If the…

A: Given that, at t=55, covered part= s(t)= 47 meters. So the point is (55,47) For velocity at the…

Q: use the method in Example 3 to find (a) the slope of the curve at the given point P, and (b) an…

A: y=x2-2x-3

Q: Suppose the position function for a free-falling object on a certain planet is given by s(1) =-…

A: Given: st=-14t2+v0t+s0

Q: #2.) Calculate the slope of the tangent to the given function at the given point or value of x b.)…

A: 2.b) gx=x+2, P-1,1d) fx=5x-2, P4,52 Note:     multiple questions are given, we are answer only one…

Q: Q3:) The point moving on the curve y = x³ - 3x+ 5, such that * +3, where (t) represents time. What…

A:

Q: 5. Find the slope of the tangent to the function b hor-0-s1= -S= xb 6 Ⓒ-(²-x) at x=1 Yo For-V xb

A:

Q: use the method in Example 3 to find (a) the slope of the curve at the given point P, and (b) an…

A: Given equation of curve :                                       y = x3

Q: Find the linear velocity of a point moving with uniform circular motion, if the point coversa…

A: Given: distances=30 miles and timet=2 hours we know that velocity v is given by…

Q: 1. Find the equation of the tangent line to x? + y? = 9, at the point (2, v5). %3D

A:

Q: The displacement (in meters) of a particle moving in a straight line is given by s = 2 - 9t + 15,…

A:

Q: .3 ax when x= For what values of a and b is the line -3x + y = b tangent to the curve y 4? b

A:

Q: Find for x? + x +y² + 2 = 3xy the lines that are tangent and normal to the curve at point (3,2).

A:

Q: Q.3 a).Find equations of the tangent line and normal line to the curve y =x} - x+ 2 at the point (1,…

A: First find slope at given point then use equation of line

Q: The curve y = ax2 + bx + c passes through the point (1, 2) and is tangent to the line y = x at the…

A:

Q: Find the direction in which f(x, y) = x/y2 increases most rapidly at the point p=(3, −1). .b) What…

A:

Q: Q3 Given the following function, determine the maximum rate of change of it at the point P(0,0,…

A: For a three-dimensional function f(x,y,z), the maximum rate of change of the function at the point,…

Q: 19. Find an equation of the tangent line to the graph of f(x) = 2/x at (a) (1, 2); (b) (–1, –2); (c)…

A:

Q: A particle is moving along a straight line such that when it is at the origin it has a velocity vo.…

A:

Q: Q3:) The point moving on the curve y = x - 3x+5, such that ****, where (t) represents time. What is…

A:

Q: Find the slope of the tangent line to the ellipse (x2/36) + (y2/49) = 1 at the point (x,y). slope =…

A:

Q: The temperature at a point (x, y, z) is given by T(x, y, z) = 1300e –2y²–2² %3D where T is measured…

A: The rate of change of a function at a point P in the direction of another point Q is nothing but the…

Q: A particle moves along a straight line with its position given by s(t) = -8t2 + 16t + 1. Find its…

A:

Q: 5. Find the slope for f(x, y) = xey at P (2,0) in the direction of the line from M(2,0) to N(-1,2)

A: To find the slope for function f at point P in the direction of the line from M to N.

Q: 3. Find the slope of the tangent line to x? = (y² + 1)(x + y) at (0,0).

A: As we know that: The slope of the tangent line to the given curve is equal to the derivative of the…

Q: Find (a) the slope of the curve at the given point P, and (b) an equation of the tangent line at P.…

A:

Q: The price (in dollars) of a computer component is P = 2C − 18C−1, where C is the manufacturer’scost…

A: To determine the rate of change of price with respect to time at t=3.

Q: Consider the parabaloid given by z = 3+x2 + 5y². a. Assume that you are standing on this parabaloid…

A:

Q: T(x, y, z) 1000e -x²–2y? –22 where T is measured in °C and x, y, and z in meters. 1. Find the rate…

A:

Q: 4) Find a formula for the line tangent to the curve at the point (4,4).

A:

Q: Suppose the position function for a free-falling object on a certain planet is given by s(t)= – 131+…

A: In this we have to find out the derivative of position function so that we can get velocity so I'm…

Q: Suppose the position of an object moving in a straight line is given by the specified function. Find…

A:

Q: What is the slope of the tangent line to the curve y=v(x-2) at the point (6,2)? 1/2 (E) None of the…

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: 5x What is the slope of the tangent line to the curve y = at the point (2,2)? x2+1

A: Find the slope of the tangent line.

Q: From the following answer what is asked: f(x,y) = x√y ,(2,4), v = 2i - j d) In which direction is…

A:

Q: 5. Find the slope for f(x,y) = xey at P (2,0) in the direction of the line from M(2,0) to N(-1,2)

A: A scalar function f(x,y) is a rule that is used to associate a number or quantity with a particular…

Q: Find an equation of the tangent line to the graph at the given point. 3(x2 + y?)² = 100(x² – y²),…

A: Given that       the equation is 3(x2 + y2)2 = 100(x2 - y2) The point is (x1, y1) = (4, 2) We have…

Q: Find the linear velocity of a point moving with uniform circular motion, if the point coversa…

A: Given: s = 10 ft and t = 5 min

Q: A particle moves along a vertical coordinate axis so that its position at any time between 0 and 10…

A:

Q: 2(x² + y? )° = 25(x² – y}) at the point (3, 1). When the equation of this tangent line is written in…

A:

Q: The curve y= ax² + bx +c passes through the point (1,2) and is tangent to the line y = x at the…

A:

Q: At the point (a, b) the curve æ = t2 – 4t, y = t2 + 2t, teR has a tangent line having slope 2. What…

A:

Q: What is the slope of the tangent line that touches the graph of In y + e2¤¬1 = 3y – 4x at the point…

A: Given query is to find the slope of the tangent.

Q: Find an equation of the tangent line to the curve 2(2² + y?)? = 25(x² – y²) (a lemniscate) at the…

A:

Q: S(t) = (t + 2)² – 5, where the height is measured in feet and time in seconds. Find the average…

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Q: Find the distance s covered by a point moving with linear velocity v for the given time t.   v = 45…

A: To find: The distance covered by a point. Given: The velocity of the point is 45 mih and time is 12…

Q: 2. Consider the function y(x) = 5x² over the interval [0, 10]. (a) If the points A(0, y(0)), B(5,…

A: As per guidelines, we will solve first three subparts; Given function is yx=5x2  over the interval…

Q: From the following answer what is asked: f(x,y) = x2 e-y , (3,0), v = 3i + 4j d) In which…

A:

Q: 6. Given the curve y = x/x at what point on the curve is the tangent parallel to the line 4x – y + 6…

A: We will use differentiation and slope of line to solve this.

Q: Where on the curve of 1 does the tangent have the greatest positive slope? y = 1+ x? O 1) 3 3 O 2) 3…

A: