Assume that the temperature at all points in the cube Q = [-1,1]×[-1, 1] × [-1, 1] is proportional to the square of the distance from the origin. (a) What is the average temperature? (b) At which points of the cube is the temperature equal to the average temperature?

Q: What is the direction in which the function f(x, y) = yx - increases most rapidly at the point (-2,…

A: Given: f(x,t)=yx2-x/y2      at (-2,1)

Q: ii. find the equation of the tangent line to f at x = a. (a) f(x)=3-4x, a=2. (b) ƒ(x)=x² +x, a = 2.

A: We have to determine the equation of tangent line

Q: Suppose that the amount of energy E(x,y, z) emanating from a source at (0,0,0) is inversely…

A:

Q: Find the points where the tangent is parallel to y=0. y=x*-8x°+22x2-24x+9 O E 0 (1,1),(2,2),(3,0) O…

A: Given: y=x4-8x3+22x2-24x+9 And y=0, represents the x-axis. The Power law: ddxxn=nxn-1

Q: y = −2x4 + 4ax³ - 5x² - 8x + 1

A: Solution:-

Q: Given f (8)-3, f'(8)--5, find the equation of the tangent line at x - 8 a) y+3 (x-8) b) Oy +5 -3(r -…

A: We have been given f(8) = 3 and f'(8) = -5 and we need to find the equation of tangent line x=8.

Q: Determine the value(s) of x where the tangent to g(x) = (x + 5)(x2 - 1) is parallel to y = -7x - 8

A:

Q: The slope of the tangent line to the graph of the function y = 3/I – 6 at (36, 12) is, O -0.67 O…

A: Given function is y=3x-6. We have to find the slope of function at point 36, 12   Slope=dydx…

Q: Find the gradient of the function at the given point.

A:

Q: Find all values of x for which the tangent line of f(x) = /x² + 18x+96 is horizontal. A 0,-9 B 0,9 С…

A:

Q: Find the equations of the two tangent lines to the graph of f that pass through the indicated point.…

A:

Q: What is the slope of the tangent line to f (x) = 2" +1 at x = 2? O a) 1.5 O b) 3.2 c) 5.1 d) 2.8

A: Solution

Q: The equation of the tangent line for the function f( O y = -7 O y = -7(x – 4)+35 %3D O y = -7(x+ 4)…

A:

Q: Find the rightward-pointing (positive x-direction) unit tangent to the curve P = {(x, y) E R² |y =…

A:

Q: Let f(x) = x + vx . The equation for the tangent line at the point (1, 2) is y = m(x – 1) +2, where…

A: Given: fx=x+x

Q: Suppose that a, b, and c are unknown constants such that f(x) = x² + ax + b and g(x) = e(3z–3) %3D…

A:

Q: a) Find an equation of the tangent line: x' +y' + 9xy = 27 at (x, y) = (1, 2)

A:

Q: For the function z = = f(x, y) = x² − xy² + y³, find the equations of the tangent lines in both the…

A:

Q: Find the equation of the tangent plane to z=e^y+x+x^4+6 at the point (4,0,267).

A:

Q: What does it mean for a function ƒ(x, y) to be differentiable? What does the Increment Theorem say…

A: Concept:   The calculus helps in understanding the changes between values that are related by a…

Q: (b) The tangent plane to the graph of z = f (x, y) at the point (1, 0, 1) can be described the…

A: We need to find the tangent plane to the graph of f(x,y)=e3yx4 at the point (1,0,1)

Q: 1- Find the equation of the tangent to the 2(x2 + y?)2² = 25(x² . y?) %3D at (3,1)

A: To find the equation of the tangent

Q: 21 Find the value of c such that the line y = -x + is tangent to the curve y = c/x.

A: Given line ⇒y = 76x+212    .....(1)curve y = cx   ....(2)Differentiating w.r.t 'x'       (2)y' = c2x…

Q: ) Determine the slope of the tangent line to the function with the given information: a. f(x,y) =…

A:

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: Find the equation of the tangent plane to z = e + x + x³ + 9 at the point (2, 0, 20). z =

A: According to question We have to calculate the equation of the tangent plane .

Q: Find for the function defined implicitly by x?y + ay? = b, where a and dx b are fixed constant. For…

A: The given equation is x2y+ay2=b, where a and b are the constants.

Q: a) Find the equation of the tangent plane to the graph of the curve f(x,y) = x² + y² at the point…

A: Mentioned below is the answer

Q: JF and GF are tangent to OH. What is HJ? 3x-5 H X+1 2x G HJ =| (Type an integer or a decimal.)

A:

Q: The slope of the tangent line at any point (x, y) on a curve is 2,r. If the point (9, 3) is on the…

A:

Q: - Find the equation of the tangent to the 2(x2 + y?)2 = 25(x² – y2) at (3,1)

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: find an equation of the tangent plane at the given point. G(u,w) = sin(uw), ( π/6 , 1)

A: Given that: G(u,w)=sin(uw) Now, Find the partial derivatives of Gu(u,w)  and  Gw(u,w) at point π6,1.…

Q: Find the direction in which the function g(x, y) = cos(xy) decreases fastest at the point (1, pi)

A:

Q: Find the equation of the tangent plane to z= e" +x+x³ +1 the point (2, 0, 12).

A: Let a surface be represented by the function fx, y, z = c where c is a constant. Then the equation…

Q: 3. Use the Fundamental Theorem of Calculus Part I to find the derivative of a) [(cost +r +e' )dt b)…

A: “Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: The gravitational attraction F between two objects of masses m1 and m2 is jointly proportional to…

A: see the attachment for answer

Q: Find the equation of the tangent plane to z = e" + x + x² + 6 at the point (5, 0, 37).

A:

Q: a. Verify that the given point lies on the curve. b. Determine an equation of the line tangent to…

A:

Q: Find the equation of the tangent plane to z = e9 +x + x³ + 6 at the point (3, 0, 253).

A:

Q: Find the equations of the two tangent lines to the graph of f that pass through the indicated point.…

A: Given that f(x)=8x-x2 find the equation of two tangent lines

Q: Find the indicated quantities for f(x) = 2x². (A) The slope of the secant line through the points…

A: note : According to our guidline i can solve only first 3 , please reroute remaining question.

Q: In x Find the equations of the tangent lines to the curve y = at the points (a) (1,0) and (b) (e,…

A:

Q: (c) Find the equation of the tangent plane to the graph of f(x, y) at (1,1,3).

A: Suppose surface S defined by a differentiable function  z=fx,y and point Px0,y0,z0 lie on the…

Q: Find the equation of the tangent line to a? + y? = 9 at the point (2, v5) O y = 5+ 2 (x - 5) V3 Oy =…

A:

Q: If f(2) = -3, f'(2) = ÷ and g(x) = f¯(x), what is the equa %3D the tangent line to g(x) at x = -3?…

A:

Q: Find the equation of the tangent plane to z = e + x + x² + 4 at the point (3, 0, 17).

A:

Q: Let a, b, and c be constants. Find the equation of the line tangent to f(x) = (x − a)(x − b)(x − c)…

A: The given function is: f(x)=(x-a)(x-b)(x-c)

Q: Chapter 8: Prove that the surface area of a sphere is the derivative of its volume, with respects to…

A: “Since you have asked multiple questions in a single request, we will be answering only the 1st…

Q: Find an equation of the tangent plane to the graph of F (r,s) at the given point: F (r,s) =…

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.