box 13. Suppose the radius r, volume V, and surface area S of a sphere are functions of timet. dV and dt dr (a) How are related? -- dt dr dS and dt (b) How are related? - dt

Q: Consider the function 3..2 f(x, y) = cos(rxy) – a°y?. = cos(Txy) – x°y°. a) Find the equation of the…

A:

Q: Suppose L is the tangent line of y 3 tan a 2 csc x at x = Where does L intersect the x-axis? 40 O At…

A: topic - equation of tangent line

Q: 7. The point of contact for a tangent to the curve f (x) = º is (2,4). It intersects the x and y…

A:

Q: The gradient of the tangent to the curve y=flx) at the point P(2, (2)) is given by A 12) – h f(2+k)…

A: To find the gradient of the tangent to the curve y=fx at the point P2, f2.

Q: Consider an F-curve with d f = (2, 14). Find the F-value with area 0.05 to its right.

A:

Q: Find the equation of the tangent line to the graph of the function f(x) = 30 - 4In(2) at I = 1.…

A:

Q: Suppose z is a differentiable function of x and y implicitly defined by the equation E : 23 + xe² =…

A:

Q: +Inz Determine the equation of the tangent line to the graph of f(r) = V3 + 5t5 dt at x = 1.

A:

Q: a² + y? – a*y³ f(r, y) x² + y?

A:

Q: Q2) find the slop for the tangent of the function f (x) sin(xcos(x)) at x = 2n. %3D

A: To find the slope of the tangent of the function fx=sinxcosx at x=2π. Solution: The slope of a…

Q: The domain of the function y tanh z is 1, +∞). Select one: a. False Ob. True

A: To find the domain of this function, we use the fact that for any one-to-one invertible function f…

Q: 2) Find the maximum rate of change of f at the given point P and the direction in which it occurs.…

A:

Q: What is the period and domain of the basic tangent function y=tan(x)? @ *E, 2n, {x€R|x= (2k + 1)m…

A:

Q: Consider the function defined implicitly as 3x + y° = cot y. Find the gradient of the tangent line…

A: Given function is 3x+y3=coty which is defined implicitly. We have to find the gradient of the…

Q: 2. Describe the function's level uvves a) faiy) -L (2 ty) %3D 76y) = Sin(y-s) d) f(y) = tan %3D

A: We have to find the function level curves for the following function...

Q: Find the direction at which the function f(x, y, z) = x In(e – az) increases fastest at (-3,0, 0) O…

A:

Q: Suppose that the radius r and surface area S = 4pai r2 of a sphere are differentiable functions of…

A: The relation between surface area and the radius of the sphere is as below.

Q: 10. Find the equation of the tangent plane at (1. 1. 2) for the function f(x,y) = /6 – x² - y'· %3D

A: Here given function as fx, y=6-x2-y2 or  z=6-x2-y2 .....1

Q: The volume of a right-circular cone of radius r and height h isV = π/3 r2h. Suppose that r = h = 12…

A: Consider the given: Volume,V=π3r2hr=h=12 cmDifferentiate w.r.t. "r",dV=π32rdrh    ⋯⋯11cm increase in…

Q: Find the equation of the tangent line to the graph of f(x) = xcos(4x) at x= 4 Enter your answer in…

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: A ladder 22 feet long is leaning against the wall of a house. The base of the ladder is pulled away…

A: here need to find the relation between x and y using pythagorean theorm. the solution is following.

Q: 13. (a) Find the average rate of change of the area of a circle with respect to its radius r as r…

A: (a) Given: +

Q: The coordinates of a particle moving in the metric xy-plane are differentiable functions of time t…

A: According to the information given, particle is moving in xy-plane with the coordinates which are…

Q: dy Prob. 5 (a) ( ....) Given the curve x³ - xy² + y³ = 1, use implicit differentiation to find da at…

A:

Q: 1. Consider the curve F(x, y) = 0. Show that if F has continuous second derivatives, then a formula…

A: We will use chain rule of partial derivative  If F is a function of  two independent variables x and…

Q: find ta Limits ofx i integual tahan 2*+34 dn dy as a) ネー15 5 h a) None of these

A: In the question we have to find the limits of x in the given function.

Q: stlon 5 Use differential to approximate the change in the value of f(x)= ° as e goes from 2 to %3D…

A:

Q: Find the linear apporoximation of the function flW = V4-X at a= o %3D Ose L to approximate the…

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

Q: 7. Given (x, y)= x' + y² a) Find the derivative at P(1,1) in the direction of " = u,i +u ;j b) In…

A:

Q: Quertion rso, a,b €R,fiBr (la,b R cen differantiable and Cx, yJ E&c (labl] %3D Caldulate the…

A:

Q: Praw a slope field for the dtfferea- differentiation equation y = xty sketch an and approprlocte…

A: We have to draw a slope field for the differential equation given below: y'=x+y. To sketch the…

Q: 2. Consider the following function F (r, y, z) = x² + 2xyz + y² In z and the point P = (2,1, 1) and…

A: *The given function is, F(x,y,z)=x2+2xyz+y2×lnz *The point P is P=(2,1,1) *The vector u is u=i+2j-2k…

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: Consider a function defined implicitly as 7x + y² = cot y. Find the gradient of a tangent line at a…

A:

Q: Find ((dy)/(dx)) if y is a differentiable function of x and x^5+3y^4=x^5 tan y + 10

A: Given, x5+3y4=x5 tan y+10

Q: dz at the point (2, y, z) = (-2, 1,0) if z is a differentiable function of r and y related by the…

A: By using differentiation mathematics detailed solution given below

Q: curve at the given point. Jx = 1? – 2 7. at (-1, 0) ly=t -1 at (-1,0)

A:

Q: (il) Find the point in which the tangent line to the curve F-12-30)1+ 2+Int'+ k at t=1 intersects…

A:

Q: Suppose f( – 1) = 2 , f'( – 1) = 3 , and g(x) = r'f(x). The tangent line to g(x) at z 1 is given by…

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

Q: Differentiate the given function: y = In(sinh(2 z)) a) О sinh(2 ¤) 2 cosh(2 ¤) b) O sinh(2 z) 2…

A: Using the identities,         d( ln( x))dx=1xd(Sinh (x))dx= Cosh xd (ax)dx=a

Q: ose that y is a differentiable function of x defined implicitly by equation: = sin 3x + 1 dy at the…

A:

Q: dy Find for the following function de sin 0 y : ACos 0-1.

A: We have to find derivative

Q: +Inz 1. Determine the equation of the tangent line to the graph of f(r) = | V3 + 5t5 dt at x = 1.…

A:

Q: Find an equatlon of the tangent to the curve at the glven polnt. x - 9 sin(t), y t+t, (0, 0) Graph…

A:

Q: Can i get help step by step please

A:

Q: Suppose z is a differentiable function of x and y implicitly defined by the equation E : 2³ + xe² =…

A: Given function z3+xez=2-y3+lny3 cos(y+1)

Q: dR Q5:-The velocity of a particle moving in space is particle position as a function of t, if R= 2i…

A:

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: Question No. o3 Calculate the directional derivative the of 2. function $ (*,y, 5) = xy+ ya* at te…

A: